Jim Storer
Not to be distributed, sold, or used for profit.
Table Of Contents
Burrs - 19
Knot Shaped Three Piece Burrs
Wood Knot - 21
Cross Keys (a.k.a. Three Piece Puzzle) - 22
Knotted Cube - 23
Oskar's Blocks - 24
Shaekel Knot - 25
Cheers - 26
Standard Shaped Three Piece Burrs With A Single Trick
Segerblom Knot - 27
Sideways Burr - 28
Sonneveld Three Piece Burr - 29
Triple Play - 30
Standard Shaped Three Piece Burrs
Just The Three - 31
3 Piece Burr Yamaosa - 32
Three Open Windows - 33
GigaBurr & GigaBurr-2 - 34
Cubie Burr & Cubie Burr #2 - 35
Burrs With Four or Five Pieces
JA6PB - Just Another 6-Piece Burr - 36
Switch Board Burr - 37
Octo Burr - 38
Standard Six Piece Burrs
Simple 6-Piece Burr - 39
Mikado Block Puzzle - 41
Yamato Block Puzzle - 43
The Puzzle - 44
Misfit Puzzle - 45
Coffin's Improved Burr - 47
Bill's Baffling Burr - 48
L5 Notchable - 49
Computer's Choice 3-Hole - 50
Computer's Choice 4-Hole - 51
Eight Is Enough - 52
Compter's Choice 5-Hole - 54
The Piston Puzzle - 55
Computer's Choice Unique-10 - 56
L46AA Notchable - 57
Mega Six - 58
Love's Dozen - 59
139 Burr - 60
Non-Standard Six Piece Burrs
Twelve Points To Insanity - 61
Dragon Fly - 62
Butterfly - 63
Explode-A-Burr - 64
Programmer's Nightmare - 65
Holey Astigmatism - 66
U-Nam-It Burr - 67
Bill's Ball Bearing Burr - 68
Luxemburr - 69
Around The Bend - 70
Frantix - 71
Dovetail Burr - 72
Lock Nut - 73
Three Pieces Puzzle - 74
Tri Again - 75
Zauberflote - 76
Zig-Zag Knot - 77
Six Piece Plate Burrs
Chocolate Dip Burr - 78
Gordian Knot - 79
Bent Board Burr #2 - 80
Burrs With More Than Six Pieces
Japanese Shape Burrs (a.k.a. Kumiki Puzzles) - 81
Uranus - 83
Miyako 9-Piece - 84
Sydney Harburr Bridge - 85
Bill's Ball Buster - 86
Hectix (a.k.a. Hexsticks, Notched Hexagonal Sticks) - 87
Locked Blocks - 89
Block Puzzle Senior - 90
Satellite Burr - 91
H Burr - 92
Sears Tower - 94
Wausau '81 - 95
Wausau '82 - 96
Wausau 83 - 97
Wausau 84 - 98
Burry Joint - 99
Lassen Risti - 100
Old Oak Of England - 101
Lattice - 102
Quadlock1 - 103
The Pacco Puzzle - 104
Q.E.D. - 105
Miyako 21-Piece - 106
Binary Burr - 107
Multi Burrs
Four Burr Stick - 108
Four Burrs - 110
Lost Day (a.k.a Eight Burrs) - 111
Berserk BurrCirc - 112
Framed Burrs
Oskar's Cube - 114
Two Piece Oddity - 115
Three Sticks Trapped - 116
Three Trapped Sages - 117
Pandora's Box (a.k.a. Internal Combustion) - 118
Locked Sticks - 121
Burr Sets
Simple 6-Piece 6-Solutions Burr Set - 122
Burr Set JCC - 123
CCH Level 1 Key Piece Burr Set - 124
Interlocking Puzzles Burr Set - 126
Interlocking Puzzles Burr Set #2 - 130
Cube Assembly - 133
Pieces Made from Unit Size Cubes
Soma Cube - 134
Half Hour - 135
IP Five Piece Cube - 136
Coffin Quartet - 137
Four X - 138
Bedlam Cube - 139
Century Cube - 140
Pieces Made from Rectilinear Non-Cubic Shapes
Patio Block - 142
Patio Block MPA - 143
Splitting Headache - 145
Pieces Based on Polyhedral Dissections
Quadro Cube - 146
Diagonal Cube - 147
Pieces With Interlocking Connections
Cubes And Pegs - 148
Cubes And Pegs Version B - 149
L-Bert Hall - 150
Five Minute Puzzle - 151
Corner Block - 152
Pieces Of Eight - 153
Groovy Cubes - 155
Twenty Cube - 156
Rik's Kiddy Wrapping - 157
Manipulation of Connected Cubes
Folding Cubes - 158
Hinged Cubes - 159
Kev's Snake Cubes (a.k.a. Serpent Cubes) - 160
Cubra Cubes - 161
Packing - 162
Checkerboard Puzzles
Checkerboard (a.k.a. All Square Novelty Puzzle, Check-A-Board, ...) - 163
Sectional Checkerboard Puzzle - 164
Chequers (a.k.a. Famous Bug House Puzzle) - 169
The Bug House Puzzle - 171
Famous Baffling Checkerboard Puzzle - 172
XceL Checkerboard Puzzle No. 1 - 173
XceL Checkerboard Puzzle No. 2 - 174
Gyro Checker Board Jig Saw Puzzle - 175
Draught Board Puzzle (a.k.a. Krazee Checkerboard Puzzle, Zebas Puzzle,...) - 176
Adams Idiot's Delight Checkerboard Puzzle - 179
Japanese 19 Piece Checkerboard Puzzle - 180
Richter Tangram and the Other 36 Anchor Stone Puzzles
Anchor Puzzle Tangram (a.k.a Caricature, Cut-Up Square ... Richter No. 8) - 181
The Nine (a.k.a. All Nine, Richter No. 1) - 190
Lightning Conductor (a.k.a. Richter No. 2) - 192
Egg Of Columbus (a.k.a. Columbus' Egg, Columbian Puzzle, Richter No. 3) - 195
Patience Prover (a.k.a. Richter No. 4) - 197
Trouble Killer (a.k.a. Richter No. 5) - 199
Heart Puzzle (a.k.a. Richter No. 6) - 202
Kobold (a.k.a. Richter No. 7) - 204
Circular Puzzle (a.k.a. Richter No. 9) - 205
Cross Puzzle (a.k.a. Richter No. 10) - 208
Not Too Hasty (a.k.a. Richter No. 11) - 212
Pythagoras (a.k.a. Richter No. 12) - 215
Tormentor (a.k.a. Richter No. 13) - 220
BeQuiet (a.k.a. Richter No. 14 /3) - 224
Sphinx (a.k.a. Lott's Stone Puzzle, Richter No. 15 / 16) - 226
Magic Egg (a.k.a. Miracle Egg, Richter Anchor Stone Puzzle No. 16 / 17) - 229
Wrath Breaker (a.k.a. Richter No. 17) - 231
Richter Anchor Stone Puzzle No. 23 - 234
Richter Anchor Stone Puzzle No. 26 - 235
Richter Anchor Stone Puzzle No. 27 - 236
Richter Anchor Stone Puzzle No. 30 - 237
Richter Anchor Stone Puzzle No. 35 - 238
Richter Anchor Stone Puzzle No. 36 - 239
Richter Summary - 240
Some Other Richter Puzzles and Games
Richter Piccolo Nr. T1 (a.k.a. Richter Picco Nr. T1) - 248
Richter Star Puzzle - 249
Richter Meteor 1 - 252
Richter Meteor 6 - 253
Other Tangram-Like Puzzles
Daddling - 254
Pythagoras - 255
Voodoo - 256
HiHo - 257
Sherlock Holmes - 258
Scrambled Egg - 259
121 Puzzles - 260
ELZZUP - 261
King Tut's Puzzle - 266
HIQU - 267
Shape By Shape - 268
Other 2D Puzzles With Polygonal Shapes
Four Piece Square (a.k.a. Magic Square) - 269
Double Square (a.k.a Square Me, Five Block Puzzle, Madagascar Madness) - 270
Missing T (a.k.a. T Puzzle, Magic T, Cut-Up T, Pa's T Puzzle - 273
H Puzzle - 276
Pie Without E - 277
Make A Square - 278
Other 2D Packing Puzzles
Krazee Links (a.k.a Endless Chain) - 279
Batee Baseball - 280
Blockade - 281
Pencil Puzzle - 282
Pearl In The Shell - 283
Czech Farms - 284
Pentominoes
Pentominoes (a.k.a Polyominoes) - 285
Twin Box Pentominoes - 293
3D Box Filling
Block Head (a.k.a. Sneaky Squares, Stark Raving Cubes, Square Fit, KUBI) - 294
Three Piece Block Head (a.k.a. The Third Degree) - 295
Log Stacker - 296
Dice Packing Box - 297
Pack It In - 298
Parcel Post - 299
Bermuda Hexagon - 300
Matching - 301
2D Matching
Rubik's Tangle 3x3 (a.k.a Rubik's Mini Tangle) - 302
Rubik's Tangle 3x3 Double Sided - 303
Rubik's Tangle 5x5 - 304
Crazy Puzzles - 305
Lost Rope - 306
Drive Ya Nuts - 307
Circus Seven (a.k.a. Mind Exerciser) - 308
Circus Puzzler (a.k.a. Color Matcher) - 309
Color Match - 310
Thinkominos - 311
Match The Colors - 312
Triazzle - 313
Bee - 314
Invisible - 315
Snake Pit - 316
Frog Pond - 317
Tool Trouble - 318
Transposer 6 & Bonbons - 319
Transposer Kaboozle - 320
Tantrix Discovery - 321
Tantrix Extreme - 322
Great Gears - 324
Spectra - 325
Instant Insanity Family
Instant Insanity (a.k.a Katzenjammer, Great Tantalizer, Face-4, ...) - 327
The Grand Army Puzzle - 340
The Allies Flag Puzzle (a.k.a. The Allied Flags Puzzle) - 341
The Allies Flags Puzzle - 342
Iribako - 343
Drives You Crazy - 344
Boer War Puzzle - 345
Other 3D Matching
Bolygok - 347
Double Disaster - 348
Mental Blocks - 349
Disney Cubes - 350
Make A Dice (a.k.a. Spots Puzzle) - 351
Twice Dice - 352
Loony Tunes Blocks - 353
Smarts Pyramid - 354
Smarts PyramidJr - 355
The Rock - 356
Einstein Cube - 357
Rubik Triamid - 358
Other 3D Shape Assembly - 359
Convex Polyhedral Shapes
Two Piece Pyramid (a.k.a. Magic Pyramid) - 360
Three Piece Tetrahedron - 361
Four Piece Pyramid, Version 1 - 362
Four Piece Pyramid, Version 2 - 363
Four Piece Tetrahedron - 364
Truncated Tetrahedron - 365
Five Piece Tetrahedron - 366
Truncated Octahedra - 367
Truncated Cubes - 368
Garnet - 369
More Complex Polyhedral Shapes
Three Piece Block - 370
Three Boxy - 371
Three Pairs - 372
Augmented Four Corners - 373
Turnabout - 374
Triumph - 375
Fusion Confusion - 376
Rosebud - 377
Twelve Piece Separation - 378
Crystal Pyramid - 381
3D Jig Saw Puzzles
Jig Saw Dog - 382
Wonder Puzzle Block - 383
3x3 Chinese Zigzag - 384
3x4 Chinese Zigzag - 385
Four Piece Jig Saw Puzzle - 386
Wonders Of The World Cube Puzzle - 387
Misc. Shape Assembly
Oskar's Matchboxes - 388
Pegged Puzzle - 389
Wood Star - 390
Saturn Ring - 391
Rubik's Snake - 392
Yin And Yang - 393
Rubik's Cube Etc. - 394
Rubik's Cube
Rubik1x2x2 - 395
Rubik 1x3x3 Floppy Cube - 396
Rubik1x3x3 Floppy Mirror Cube (a.k.a. Magic Floppy Cube) - 397
Rubik1x3x3 Scramble Cube - 398
Rubik's 2x2x2 Pocket Cube - 399
Rubik 2x2x2 Bandaged - 406
Rubik 2x2x2 Double Bandaged - 407
Rubik 2x2x2 Nested (a.k.a. Rubik 2x2x2 Super Square) - 408
Rubik 2x2x2 Cubes Fused - 409
Rubik 2x2x3 Tower Cube (a.k.a. Slim Tower, Franken Tower) - 410
Rubik 2x2x4 Tower - 411
Rubik 2x3x3 Domino - 412
Rubik2x3x3 Layered - 413
Rubik's 3x3x3 Cube - 414
Rubik 3x3x3 Mirror Cube (a.k.a. Mirror Block, Yong Jun Cube) - 420
Rubik3x3x3 Fisher Cube (a.k.a. Square King) - 421
Rubik 3x3x3 Void Cube (a.k.a. Holey Cube) - 422
Rubik 3x3x3 Edges Only (a.k.a. Cornerless Void Cub) - 423
Rubik's 3x3x3 Fourth Dimension - 424
Rubik 3x3x3 Layered - 425
Rubik's 3x3x3 Perpetual Calendar - 426
Rubik 3x3x3 Bandaged (a.k.a. Bicube) - 427
Rubik 3x3x3 Patched (a.k.a. Fused Cube) - 428
Rubik 3x3x3 Brick (a.k.a Brick Cube) - 429
Rubik 3x3x3 Latch Cube - 430
Rubik 3x3x4 - 431
Rubik 3x3x9 - 432
Rubik 3x3x9RoadBlock - 433
Rubik 3x4x5 - 434
Rubik 4x4x4 Revenge - 435
Rubik 5x5x5 Professor - 436
Rubik 6x6x6 (a.k.a. V-Cube 6x6x6) - 437
Rubik 7x7x7 (a.k.a. V-Cube 7x7x7) - 438
Large Rubik Cubes - 439
Evil Cuboids
Evil Cuboid 2x3x4 - 440
Evil Cuboid 3x3x3 - 441
Evil Cuboid 3x4x5 - 442
Crazy Cubes
Crazy Cube 2x3x3 - 443
Crazy Cube 3x3x3 - 444
Crazy Cube 3x3x7 (a.k.a. WitEden Super Magic Cube) - 445
Crazy Cube 4x4x4 - 446
Crazy Cube 4x4x4 Two - 447
Other Rectangular Shapes
Axel Cube - 448
Skewb - 449
Holey Skewb (a.k.a. Void Skewb) - 451
Golden Cube - 452
Dino Cube (a.k.a. Dinosaur Cube) - 453
Blue Magic (a.k.a. Black Flower Cube, Star Cube, Rex Cube) - 454
Mosaic Cube - 455
Square 1 (a.k.a. Super Cubix, Cube 21) - 456
Helicopter Cube - 464
Gear Cube - 465
Gear Cube Extreme - 466
Gear Shift - 467
Pyrmid and Diamond Like Shapes
Pyraminx - 468
Jing's Pyraminx (a.k.a. Rounded Halpern-Meier Pyramid) - 470
Crazy Pyraminx (a.k.a. Crazy Tetrahedron Plus) - 471
Tetraminx - 472
Professor Pyraminx - 473
Vulcano - 474
Megaminx (a.k.a. Supernova) - 475
Holey Megaminx - 476
Crazy Megaminx - 477
Kilominx (a.k.a. Flowerminx) - 478
Master Kilominx - 479
Gigaminx - 480
Teraminx - 481
Pyraminx Crystal - 482
Skewb Diamond - 483
Super Skewb Diamond (a.k.a. Diamond Octahedron) - 484
Skewb Ultimate - 485
Skewb Kite - 486
Skewb Fourteen - 487
Pyrastar - 488
Pyramorphix (a.k.a Figurenmatch, Distortion Demon Square) - 489
Starburst (a.k.a. Star of David, Sterns Puzzle) - 490
Mastermorphix (a.k.a. Master Pyramorphinx) - 491
Pillow Cube (a.k.a. Cushion Cube) - 492
Enhanced Pillow Cube (a.k.a. Polish Cushion) - 493
Confused Pillow Cube - 494
Hungarian Diamond - 495
Rhombi Diamond (a.k.a. Diamond Style Puzzler) - 496
Octahedron (a.k.a. Magic Octahedron) - 498
Full Octahedron - 499
Flowered Jewel (a.k.a Jewel Puzzler, Christopher's Magic Jewel, ...) - 500
Disc and UFO Shapes
Rubik's Cheese - 501
UFO Cheese - 502
Rubik UFO - 503
Puck Puzzle (a.k.a Hockey Puck Puzzle) - 504
Saturn - 505
Hungarian UFO (a.k.a. Varia Disk) - 506
Tricky Disky (a.k.a. Tricky Disk, Mind Trapper) - 507
Smart Alex (a.k.a Alpa-2-Go) - 508
Netblock UFO / Sando Ring (a.k.a. King Ring) - 509
Octo (a.k.a. Meeting Colors, Disco Puzzle) - 510
Gerdig UFO - 511
Brain Ball - 512
Sphere Shapes
Rubik 2x2x2 K-Ball - 513
Rubik 3x3x3 Ball - 514
Rubik 3x3x3 Apple - 515
Master Ball (a.k.a. Duo Master, Geo Master) - 516
Skewb Puzzle Ball (a.k.a Creative Puzzle Ball) - 519
Impossiball - 521
Dogic - 522
Other Shapes
Rubik Barrel - 523
Cuboctahedron - 524
Rainbow Cube - 525
Dino Star - 526
Alexander's Star - 527
Platypus - 528
Skewb Egg (a.k.a. Golden Egg, Silver Egg, etc.) - 529
Brain Twist - 530
Roundy - 531
Other 3D Manipulation - 532
Panel Puzzles
Rubik Mini Magic Panels (a.k.a Rubik Magic Junior) - 533
Rubik's Magic Panels - 538
Rubik Magic Panels Create The Cube - 546
Rubik's Master Magic Panels - 548
Rubik Magic Cross Panels - 550
Rubik Super Magic Panels - 551
Towers Of Moving Balls Or Tiles
Whip-It Towers (a.k.a. Genius Puzzle) - 553
Varikon Towers - 554
Whip-It Ball - 556
Babylon Towers - 557
Calendar Bank - 558
Thai Tower (a.k.a. Clever Toys Tower) - 559
Numbers Barrel - 560
Missing Link - 561
Reduced Missing Link - 563
Extended Missing Link - 564
Doubled Missing Link - 565
Mini Missing Link - 567
Other Puzzles With Moving Balls or Tiles
Hungarian Globe (a.k.a. Equator Ball, Magic Sphere, IQ Ball) - 568
Magic Sphere - 570
Touchdown - 571
Twister (a.k.a. Wooden Screwball, Clever Toys Natural) - 572
Atomic Chaos (a.k.a. Kaos) - 573
Entrapment - 574
Pakovalec (a.k.a. Stupid Cylinder) - 575
Ten Billion Barrel (a.k.a. Billion Barrel, Tumbler Puzzle) - 576
Russian Revolver (a.k.a. Russian Flower, Russian UFO, Soviet UFO) - 577
Back Spin (a.k.a. Loophole) - 578
Sliding Piece Can Puzzle - 579
Sliding Piece Can Puzzle - 580
Brain Racker - 581
The Orb (a.k.a. Orb-It, l'ORBS) - 582
Rubik's Shells - 583
Astrolabacus - 584
Movement of Pieces by Tilting or Pushing
Varikon Box 2x2x2 - 585
Varikon Box 3x3x3 - 586
Inversion - 587
Peter's Black Hole / Vadasz Cage (a.k.a. Inside Out, Magic Jack, IQ Cube) - 588
Mad Marbles - 589
Dice Box - 590
Clark's Cube - 591
Pionir Box (a.k.a. Pionir Cube) - 592
Rubik Dice - 593
Movement of Discs and Rings
Towers Of Hanoi (a.k.a. Pyramid Piling Puzzle, Brahma Puzzle) - 594
Chinese Rings (a.k.a. Cardan's Rings, Baguenaudier) - 597
Spinout - 601
Hexadecimal Puzzle - 602
WanderRings - 606
Panex - 608
Manipulation Of Positioned Balls, Levers, Buttons, Etc.
Cmetrick - 609
Cmetrick Too (Hard) - 610
Planets - 611
SaturnLD - 612
Orbik - 615
Cross Teaser - 616
Rubik's Clock - 617
Cerebral Rings Puzzler - 619
Misc.
Wisdom Ball (a.k.a. Mind Twister) - 620
SpongeBob PuzzlePants (a.k.a. SpongeBob Cube) - 621
Flip Side - 622
Kabalabda - 623
Rubik's Rabbits (a.k.a. Rubik's Hat) - 624
Enigma - 625
Sliding Pieces and Other 2D Manipulation - 626
Square Pieces
Fifteen Puzzle - 627
Sixteen Puzzle - 666
Nine Puzzle - 667
Ditho (a.k.a. Fourteen Puzzle) - 669
Great Fifty Puzzle - 672
Panama Canal Puzzle - 673
Moving Day (a.k.a. a.k.a. 5-Block Puzzle, Lodging House Difficulty) - 677
Bull's-Eye (a.k.a. Target) - 678
Good Luck - 679
Twenty - 680
Double Trouble Puzzle - 681
Twenty Seven - 682
Cornell Crossword Puzzle - 684
Thirty One (a.k.a. Jumble) - 685
SKOR - 687
Missionary Puzzle - 688
Mystic - 689
Square Pieces WIth Obstacles
Grandpa's Car (a.k.a. Slide-Blocked Sliding Block) - 690
Time Puzzle - 691
Work Or Golf (a.k.a. Motor Garage Puzzle, Parka Car, Sputnik, E Peg Puzzle) - 693
Honor And Glory (a.k.a. Black And White) - 694
1x1 and 1x2 Pieces
Get My Goat (a.k.a. Kapture The Kron Prinz, Boogie Man, Center Point, ...) - 695
Line Up The Quinties - 700
Johnson City Puzzle - 702
Four Suits 2 - 704
Slidem WWII Puzzles - 705
Monarch - 709
Dad's Puzzler Family
Dad's Puzzler (a.k.a. Moving Puzzle, Tit-Bits Teaser 1, Penant Puzzle, ...) - 710
Dads Puzzler - Humdinger Version - 736
Dad's Puzzler - Exchange Version / Infants' Hospital Puzzle - 743
Quzzle And Quzzle Killer - 750
Nine Block - 754
Red Donkey, with Simple TJ, Century, Super Century (a.k.a. L'Ane Rouge, ...) - 757
Traffic Jam / Let Me Through - 767
Century and Super-Century - 772
Grand Master With Century And A Half and Little House - 778
Ushi And Ushi-Flipped - 785
Hole In One With Royal Out and King Out - 788
Fence The Cow - 791
Dad's Puzzle Family Set With Fujiwara 15/22/25 and Super Compo - 793
Beyond Dad's Puzzler Family
Infants Hospital Puzzle (a.k.a. Infants Progress Puzzle) - 798
Trans-Atlantic (a.k.a. Ten Block Puzzle, Traffic Cop Tangle) - 800
Happy Couple (with Ten Block and The Hughes Puzzle) - 801
Flying Puzzle (a.k.a. Starry Puzzler, Tit-Bits Teaser No. 2, Ching Foo, ...) - 806
Technocracy - 816
George Washington Puzzle - 817
Tit Bits Teaser No. 5 - 820
Century Of Progress - 822
Sliding Block Puzzle (a.k.a. Fifteen Block Puzzle, 1-2-3 Puzzle, ...) - 823
Slide A While & Model Garage - 827
Tokyo Parking / Rush Hour - 832
Further Beyond Dad's Puzzler Family - Non-Rectangular Shapes
Ma's Puzzle (a.k.a. Spirit of '76, Wooden Puzzle, Rectangle Puzzle) - 836
Mini Ma - 843
Traffic Jam Puzzle (a.k.a. Tit-Bits Teaser No. 4) - 844
Slider (a.k.a. Hole In One) - 851
Heart-In - 852
Soap - 853
Block Ten - 854
Neo Black And White - 860
Neo Pink And Blue - 865
Kuroko And Dairu - 867
Dinosaur Egg (a.k.a. Egg Puzzle) - 868
Dog And Cat - 869
RunAway - 870
Trap - 871
Tricky - 878
Two Sliding Squares - 886
Movement of Buttons, Balls, Numbers, etc.
New Fifteen Puzzle - 887
Perplexity Puzzles (Perplexity, Automobile, This is Jonah, Panama Canal) - 888
One To Ten - 889
Good Luck Railroad Puzzle Game - 890
Rotos - 891
Puzzler Novice / Challenge / Avenger (a.k.a. Turnstile, Twinspin, ...) - 892
Rotascope (a.k.a. Taquinoscope) - 893
Hungarian Rings - 895
Hungarian Rings Triple - 896
Hungarian Rings Quad - 897
Hungarian Olympic Rings - 898
Billiards - 899
Billiards 9-Ball - 900
Flower - 901
Trio - 902
Trio 2 - 903
Butterfly - 904
Movement of Tokens
Eight Peg Puzzle - 905
TeeZ / Brain Buster - 906
Peg Puzzle - 907
Hopper (a.k.a. Downsize) - 908
Mechanically Assisted Sliding Pieces
Top Spin / No. Crunch - 910
Magic Cross (a.k.a. Zauberkreuz) - 911
Rubik's XV (a.k.a. Rubik's Fifteen) - 912
Tsukuda's Square (a.k.a. It, 4x4 Four By Four Puzzle) - 913
Uriblock (a.k.a. Mix Box) - 914
Trillion - 915
Port To Port And Triple Cross - 917
Switch Back - 918
SwissMad - 919
Mad Triad Challenge (Twisting Tri-Side Puzzle) - 920
Mad Triad Handy (Twisting Tri-Side Puzzle) - 921
La Cerradura Doble - 922
String and Wire Puzzles - 923
Move or Remove a Ring
Horse Shoes - 924
Ball And Ring (a.k.a. Ball And Chain) - 925
Moving Rings (a.k.a. Moving Beads, Tiger Cross) - 926
Wits End - 927
Single Loop Wit's End - 928
Loop Trap - 929
Parallel Dimension - 930
Disengage Two Pieces
Wire U's - 931
Wire P's - 932
Wire Heart - 933
Vortex - 934
Simple Knot 47091 - 935
EZ Atom 47092 - 936
Lucky Clover - 937
Misc.
Rod and Loop - 938
Hide The Knots - 939
Other Puzzles - 940
Mechanicl Challenges
TakitaparT (a.k.a Take It Apart) - 941
Double Puzzle - 942
Rook Puzzle - 943
Bolt And Ball - 944
Cage Puzzle - 945
Drive The USA - 946
Screwball - 947
Magic Chalice - 948
Dexterity Puzzles
Abercrombie & Fitch Dexterity Puzzles - 949
A Ward In The Infant's Hospital - 950
ElsieCow - 951
Reiss Style 393 - 952
Crazy Maze - 953
Springs And Balls - 954
Brain Teasers
What's Your Age - 955
Puzzle Boxes
Parrot Box - 956
Spin Box - 957
Stickman Fulcrum Box - 958
Games - 959
Goblet - 960
Quixo - 963
Quarto - 964
Othello - 965
Nine Mens Morris (a.k.a. Mill, Muhle, Merelles / Merilles, Mulino) - 966
Tablut - 968
Senet - 970
Nannon (a.k.a. Nano Backgammon) - 974
Make Numbers - 975
Books - 976
Hoffmann's Puzzles Old and New (1893) - 977
Hordern's Edition Of The Hoffmann Book - 983
Hoffmann Posthumous Books - 984
Hoffmann's Best Math Book - 985
Hoffmann Study Book - 986
Hoffmann's Magic Trilogy Books - 987
Robert Merry's Books Of Puzzles 1-3 (1866) - 988
Excursions Into Puzzledom (1879) - 989
Everybody's Puzzle Book (1890) - 990
New Book Of 200 Puzzles (1908) - 991
Dudeney Books (1920's) - 992
Dudeney Posthumous Books - 993
Sam Loyd's Cyclopedia Of Puzzles (1914) - 994
Sam Loyd and His Puzzles (1928) - 995
Wyatt's 1928 and 1946 Books - 996
Johnson Smith Catalog (reprinted from 1929) - 997
Hirschberg Book (1930) - 998
Filipiak Book (1942) - 999
Everythings A Puzzle - 1000
Bell's History of Board Games - 1001
Murray's History of Board Games - 1002
Winning Ways Books - 1003
Hordern's Sliding Puzzle Book - 1004
The Mathematics Of Games - 1005
Slocum and Botermans Books - 1006
Coffin's Book On Polyhedral Dissections - 1007
Coffin's Puzzle Craft Books - 1008
Cutler's 6-Piece Burr Books - 1009
The Puzzle Archade - 1010
Frederickson's Dissections Book - 1011
G4G Tributes To Martin Gardner - 1012
The Follette Puzzle Design Book - 1013
The Tangram Book - 1014
Haubrich's Checkerboard Puzzles - 1015
The Fifteen Book - 1016
A Visual History of The S.S. Adams Co. - 1017
The Self and Lensch Puzzle Design Book - 1018
Boardman's Puzzle Projects Book - 1019
The Anchor Puzzle Book - 1020
Pieces are formed by removing unit cubes from rectilinear solid pieces. A burr is notchable if it can be made with just straight cuts. Some burrs have a "key" piece that slides out. More complex ones have a number of internal voids (called holes) or spaces between pieces, where removing the first piece may require sliding several pieces. An assembly of a burr is a configuration of the pieces in the solved shape. An assembly is a solution if it can be achieved by starting with the pieces apart and making legal moves. The level of a solution is the minimum number of moves required to remove the first piece (or separate the puzzle into two pieces). The level of a burr is the lowest level of its solutions. Note that to compute level, we use Cutler's definition, where the movement of several pieces together, or the consecutive movement of pieces in the same direction, counts as a single "move".
Rob's Puzzle Page, from: http://home.comcast.net/~stegmann/interlocking.htm
Cutler's Holey 6PB Booklet, from: http://home.comcast.net/~billcutler/docs/H6PB/index.html
Cutler's Computer Analysis, from: http://home.comcast.net/~billcutler/docs/CA6PB/index.html
IBM Burr Page, from: http://www.research.ibm.com/BurrPuzzles
Curfs' Page, from: http://home.tiscali.nl/~bcurfs/homepage/burrs/burrs-e.htm
Math Games Page, from: http://www.maa.org/editorial/mathgames/mathgames_08_02_04.html
Chandler Patent, from: www.uspto.gov - patent no. 393,816
Altekruse Patent, from: www.uspto.gov - patent no. 430,502
Porter Patent, from: www.uspto.gov - patent no. 524,212
Nelson Patent, from: www.uspto.gov - patent no. 588,705
Ford Patent, from: www.uspto.gov - patent no. 779,121
Curtis Patent, from: www.uspto.gov - patent no. 781,050
Erickson Patent, from: www.uspto.gov - patent no. 985,253
Banic Patent, from: www.uspto.gov - patent no. 1,099,159
Brown Patent, from: www.uspto.gov - patent no. 1,225,760
Keiser Patent, from: www.uspto.gov - patent no. 1,261,242
Senyk Patent, from: www.uspto.gov - patent no. 1,350,039
Schenk Patent, from: www.uspto.gov - patent no. 1,455,009
Kramariuk Patent, from: www.uspto.gov - patent no. 1,542,148
Turner Patent, from: www.uspto.gov - patent no. 2,836,421
Pidgeon Patent, from: www.uspto.gov - patent no. 4,148,489
Derouin Patent, from: www.uspto.gov - patent no. 4,880,238
Dykstra Patent, from: www.uspto.gov - patent no. 5,040,797
Interlocking Puzzles,
circa 2000.
(3 wood pieces, 2.75")
Daniel C. Alsmeyer 2006,
Sabriday Puzzles.
(3 wood pieces, 3")
"Triple Cross",
Puzzles & BT 2006.
(3 wood pieces, 3.2")
Three examples of the wood knot that was patented by M. P. Rao in 1980. Here are the directions that were sold with the Sabriday version:
Further reading:
Rao Patent, from: www.uspto.gov - patent no. 4,198,053
a.k.a. Three Piece Puzzle
Purchesed from Puzzles and Brain teasers Ebay Store 2006.
(three wood pieces, 3.75 inches;
described on pages 106 and 139 of the 1983 Hoffmann book)
Designed and made by Interlocking Puzzles, circa 2000.
(walnut, paduk, and hard maple, 3 inches square)
Unlike the common three piece wood knot, there are no identical pieces:
Designed by Oskar Van Deventer, purchased from Bits And Pieces, 2008.
(metal, 1.4 inches)
Here are photographs of the three pieces being disassembled:
Here is the solution sheet that was sold with the puzzle:
Designed by Oskar van Deventer 1983.
Made by Tom Lensch.
Sold by Cubic Dissection 2005.
(three wood pieces and solution figures, 3 inches)
Designed by Ronald Kint-Bruynseels, made by Eric Fuller 2006, Level 8.
(wood, 3 inches)
Here are the 8 assembly steps:
Designed by Wilhelm Segerblom in the late 1800's.
(three wood pieces, 2.25 inches)
The IBM Burr page cites the April 1899 issue of Scientific American as publishing this puzzle. Three identical pieces each have outer dimensions 2 by 2 by 6 units. Each has all of the center 2 by 2 by 2 portion removed except for a 1 by 1 by 2 rod that is beveled at 45 degrees (a total of 7 units of wood has been removed from each piece). To assemble, all three pieces have to be slid together simultaneously (an outside surface of the rod slides perpendicular to one piece while the beveled surface slides over the corner of another). It is not possible to put two pieces together and then slide the third one in. The figure below shows the three identical pieces in the orientation to be put together.
Further reading:
IBM Burr Page, from: http://www.research.ibm.com/BurrPuzzles/
Designed by R. Stanton, made by E. Fuller 2008.
(Curly Maple, 3 inches)
Three identical piece slide together simultaneously to make a 3-dimensional cross.
Assembly: Hold one piece vertically and determine how a second piece fits (there are only a few possibilities; look for the one where two faces sit nicely together), then carefully slide it out and put that piece down on the table without disturbing its orientation, then do the same for the third piece. Now that you have determined the orientation of the three pieces, hold them in their orientations so that they are just on the verge of engaging, line everything up, and then just squeeze the three together.
Disassembly: Randomly jiggle and push on the pieces until you can get it to come apart just a bit. You can keep doing this until the puzzle comes apart, but as it comes apart a bit you should be able to find the right way to hold on to and push two of the pieces so that the puzzle slides apart, and you can just push and pull to make it expand and contract, where the third piece is being controlled by the movement of the other two that you are holding.
Here are two views of the puzzle in a partially expanded state:
Designed by Dic Sonneveld, made by Tom Lensch, circa 1990.
(Walnut, 2.25 inches)
Three identical pieces come apart in simultaneous motion:
Designed by Jim Gooch,
made by Eric Fuller,
purchased from www.cubicdissection.com.
(three wood pieces, 2.9 inches)
At first this appears to be a three piece burr made with excess play in the fit. However, the extra play is just enough so that these three identical pieces come apart with a non-rectilinear movement.
Designed by J. Krijnen, made by E. Fuller 2008, unique level 7.
(Quilted Sapelle, 3 inches)
Here are steps ito dissassemble:
Designed by O. Yamamoto, made E. Fuller 2008, unique level 4 with a twist.
(Walnut, 3 inches)
Here are steps ito dissassemble (there are two photos for the second step, which is a twist):
Designed by T. Jolly, made by E. Fuller and sold by Cubic Dissection 2008, level 6.
(Bloodwood, Wenge, Holly, 3 inches)
When assembled, one can look through the center holes in any of the three directions. Here are photographs of the six steps to disassemble, where step 2 is a twist:
Designed by Bill Cutler 1999, made by Jerry McFarland, level 8.
(left: Walnut, 2.2 inches;
right: Cherry, 2.2 inches)
The 250 billion puzzles of this type were enumerated by Bill Cutler (with a computer). The highest level (moves to remove the first piece) was 8, of which there were 80 different puzzles, where only 3 had only 9 internal voids. One is the GigaBurr, the other two are similar to each other, and one of them is the GigaBurr-2.
To solve, guess the first piece to be removed, put the other two pieces together, and then visualize the third piece in its final position to determine how to get it out (then reverse these steps to assemble the puzzle).
GigaBurr pieces
GigaBurr-2 pieces
Designed and made by Bill Cutler and Jerry McFarland 2001, level 6.
(left: Poplar / Walnut, 2.2 inches;
right: Cherry / Walnut / Wenge, 2.2 inches)
The basic design of the 3-piece GigaBurr and GigaBurr-2 was expanded to a 5x5x5 cube by gluing on edge and corner pieces. Cutler's computer search yielded three basic level 6 puzzles, of which these are two.
Designed by Bill Cutler.
(Walnut, 3.5 inches)
Four irregular shaped pieces and two ball bearings, which when assembled, look like a 6-piece burr. Falls apart easily.
Designed by Jim Gooch, made by Eric Fuller, level 9.
(Pau Amerillo / Wenge / Bocote, 3 inches)
The pieces consist of a "block", two identical "rods" in symmetric orientations, and two identical "plates" in symmetric orientations. Orientate the puzzle as shown on the left below (the right rod will drop down as shown if the puzzle is not too tight), exchange the plates by passing them through each other, then the right plate (which was the left plate) can be twisted (in two ways) and removed (or without twisting it can be slid out together with the right rod).
Designed byStewart Coffin, purchased from Cubic Dissection circa 2006.
(five wood pieces, 3.5 inches)
The 5 pieces give the appearence of four sets of two. The solution is not unique.
Old design, level 1, no holes, notchable.
(six wood pieces, 3 inches)
The basic idea of level 1 with a key piece is described on pages 106 and 139-140 of the 1983 Hoffmann book. This one is even simpler. Pieces 1, 2, and 3 are identical, pieces 4 and 5 are identical, and piece 6 is a simple solid "key" piece that comes out first.
1. 2. 3. 4. 5. 6.
Assembly:1. Place pieces 1 and 2 together to form an empty rectangle shape.
2. Lay piece 3 in the bottom of the empty rectangle.
3. Place pieces 4 and 5 on either side.
4. Slide in piece 6.
Made in Indonesia 2004.
(wood, 3 inches)
Made in Indonesia 2004.
(wood, 3.2 inches)
Purchased in the 1970's.
(plastic, 2.5 inches)
"Made by U.N. Co. N. Y.", circa 1920?, level 1, no holes, notchable, 2x2x8 pieces.
(cardboard box, 3.2 by 2.2 by 5/8 inches, and six 1/2" x 1/2" x 2" wood pieces)
Along wth the Yamato Block Puzzle, this puzzle is discussed on page 262 of the Puzzlers' Tribute Book in a chapter by Jerry Slocum and Rik van Grol on antique Japanese export puzzles. They show a picture from the 1915 C. J. Felsman Catalog of a Mikado puzzle saying "A problem of problems ...", and note that the sililar language here, "The puzzle of puzzles ...", is further evidence that although it says NY, it may in fact be a Japanese import. Here is what is on the cover and the inside of the cover:
"Made by U.N. Co. N. Y.", circa 1920?, level 1, no holes, notchable, 2x2x8 pieces.
(cardboard box, 3.2 by 2.2 by 5/8 inches, and six 1/2" x 1/2" x 2" wood pieces)
Along wth the Mikado Block Puzzle, this puzzle is discussed on page 262 of the Puzzlers' Tribute Book in a chapter by Jerry Slocum and Rik van Grol on antique Japanese export puzzles. Here is the solution sheet that came with it and a photo of another one of these puzzles where someone has labeled the pieces:
Made in Japan, circa 1930?, level 1, no holes.
(six wood pieces, each 5/16 inches square by 2.4 inches long)
Here are four basic solution steps:
"Pheno-Caffein Co.,Worchester, MA, circa 1910.
(wood, 2.1 inches)
The Pheno-Caffein Co. also made the Sectional Checkerboard Puzzle, and like that puzzle, one could obtain a solution:
Designed by Stewart Coffin level 3, 3 holes.
(six wood pieces, 3.5 inches)
Designed and made by Bill Cutler 1984, unique level 5, 7 holes.
(Red Oak, 3 inches; 24 assemblies with a unique solution)
Discovered (by computer) and made by B. Cutler 1987, unique level 5, 7 holes.
(Mahogany, 3 inches)
Discovered (by computer) and made by B. Cutler 1988, unique level 7, 3 holes.
(Cherry, 3 inches)
Discovered (by computer) and made by B. Cutler 1988, unique level 8, 4 holes.
(Maple, 3 inches)
Designed by B. Cutler, made J. McFarland 2009, unique level 8, 7 holes.
(Maple / Walnut / Cherry, 2.8 inches)
Here are the first six steps:
Now the leftmost piece can be lifted up and out:
Discovered (by computer) and made by B. Cutler 1988, unique level 9, 5 holes.
(Walnut, 3.5 inches)
Designed by P. Marineau, made by J. McFarland 1986, unique level 9, 7 holes.
(Walnut, 3 inches)
Designed by Bill Cutler 1990, unique level 10, 7 holes.
(Mahogany, 3.5 inches)
One of 18 similar unique level 10 burrs discovered by Bill Cutler with a computer program. It can be disassembled by moving (1) C /E forward 1 unit, (2) F up 2 units, (3) A back one unit, (4) D /F right 1 unit, (5) F down 2 units, (6) F forward 1 init, (7) D left 1 unit, (8) A/E back one unit, (9) B/C/F right one unit, (10) B down one unit. Note that some would consider this 11 moves since for "move" 8, both A and E can move back without dragging the other. To assemble, rather than inserting B into the pieces appropriately oriented, it may be easier to orientate things with CD facing up, and hold A/D/E (appropriately positioned) in your left hand and B/C/F (appropriately positioned) in your right hand to perform steps 10 and 9.
Discovered (by computer) and made by B. Cutler 1987, level 10, 9 holes, notchable.
(Maple, 3.6 inches)
Non-unique with solutions below level 10, but made to be unique level 10 by drawing diagonal lines on the pieces that must form a loop around the puzzle when solved.
Designed by Brian Young, made by Mr. Puzzle Australia, level 10, 8 holes.
(4.7 inches)
Unique Level 10 solution. One more hole than Computer's Choice Unique-10, with 20 assemblies instead of 7. Here is the solution that was sold with it:
Designed by Bruce Love 1987, made by Bill Cutler, level 12, 9 holes.
(Maple, 3 inches)
According to Bruno Curfs' page, Love's dozen has 89 solutions ranging from Level 3 to one of the solutions being level 12; this puzzle made by Bill Cutler has a big D drawn on a pair of the ends that forces the level 12 solution.
Further Reading
Curfs' Page, from: http://home.tiscali.nl/~bcurfs/homepage/burrs/burrs-e.htm
Designed and made by Bill Cutler; can't be disassembled.
(Red Oak, 4.5 inches)
From his computer analysis, Cutler determined that 139 was the largest number of states that a standard 6 piece burr could have without having a solution, and then he chose the simplist of these for this puzzle. So this burr is made to the dimensions of a normal 6-piece burr, has lots of movement, but can't be disassembled (it was made by gluing two portions of a piece together during assembly).
Purchased from Mr. Puzzle Australia 2006, level 1, no holes.
(six wood pieces, 3.5 inches)
Mr. Puzzle Australia credits this puzzle as being sold as early as 1875, and as having been sold under a number of names, including the Cluster, the Gem Cut Puzzle, the Chestnut Burr, and the Snowflake. When assembled it looks like a standard version of the Simple Six Piece Burr (where pieces have a diamond cross section). However, it actually is composed of six identical pieces where two assemblies of three slide together.
Made in Japan circa 1930?, level 1.
(cardboard box and 6 wood pieces, 3.75 inches;
box cover similar to other vintage Japanese exports like the Yamato Puzzle)
Made in Japan circa 1930?, level 1.
(cardboard box and 6 wood pieces, 3 inches;
box cover similar to other vintage Japanese exports like the Yamato Puzzle)
Here is the solution sheet that came with it:
Designed by Bill Cutler 1965, purchased circa 2000, level 1.
(six wood pieces, 3.5 inches)
Six identical pieces with some angled internal cuts that slide apart simultaneously.
Discovered (with a computer) and made by Bill Cutler 1989, level 5, 7 holes.
(Maple, 3.5 inches)
A programmer's nightmare because disassembly requires a twist. Move F up 1/2 unit, rotate A 90 degrees, move A up (pulling F with it by 1/2 unit), move D up, slide D out. Note that although the 1/2 move is needed theoretically, there is enough play in the puzzle that F can initially be moved up a full unit (this does not change the level since A has to be moved up in any case). This puzzle is hard for a person too, because according to Cutler's computer analysis, there are 102 assemblies (ways these pieces can exist in space in the solved shape) with only this one solution (the only way that is achievable starting with the pieces apart).
Designed and Made by Bill Cutler 1994, level 7, 4 holes, notchable.
(Cherry, 2.25 inches)
Bill Cutler credits Stewart Coffin with the idea of making burrs with slanted pieces in a way that restricts the number of possible assemblies. Cutler then found a non-unique level 7 burr from his computer analysis which became unique when made with slanted pieces. Slide F forward, slide E left (pulling D with it), slide E forward, push D right, slide F back, slide F right, remove A:
Designed by Bill Cutler.
(Walnut, 3 inches)
Slide F back and then remove the three pieces A, C , E simultaneously by expanding them out to the upper left:
Designed by Bill Cutler1986, spin + level 3.
(Red Oak with two steel ball bearings, 3.5 inches)
Spin the puzzle in the orientation shown (around the axis defined by E and F) to position the balls, and then the two halves A,C,F and B,D,E can slide apart with three moves:
Designed by Matti Linola, made by Eric Fuller 2010.
(Yellowheart and Wenge, 3 inches)
Once one sees how to solve the three piece burr formed by the light colored pieces, the dark pieces don't change the puzzle very much, but the construction and fit is terrific.
To solve:Here are photos of the assembly progressing:
- Take out the dark pieces, to first solve the 3-piece burr.
- Start with the simple U shaped piece and see that because each piece has to slide over one of the other two, there is only one way the other two can go, and then assemble the three pieces.
- Now look down each end, and it can be seen that there is only one way the dark pieces could possibly fit.
- Then take apart the three light pieces, insert the dark pieces, and push everything back together, moving the dark pieces in and out as needed.
Designed by Frans de Vreugd 2005, purchased from Mr. Puzzle Australia.
level 5, 3 hole, notchable, six 2x2x6 pieces with end caps.
(Queensland Silver Ash with Queensland Blackbean ends, 3.125")
A variation of the standard 6 piece burr where end caps have been added to the pieces; highest level for this type of burr with notchable pieces. Here is a diagram of the puzzle and the pieces (numbers are the order they can be removed):
Designed by Stewart Coffin, made and sold by Interlocking Puzzles 2000.
(wood, 2.6 inches)
A variation of the 1890 Altekruse burr with pins and holes for some of the notches; described in the Coffin Book. Disassembly is by sliding apart the two halves of the puzzle; here are photos of the halves coming apart and three pieces removed:
Designed by Frans de Vreugd, purchased from Bits and Pieces 2007, level 6.
(wood, 3.75 inches)
Designed by Stewart Coffin (design number 105)
Sold in 2006 by Cubic Dissection (www.cubicdissection.com)
(left Bocote / right Cocobola, both 3.25 inches)
Can be solved in two ways using the same pieces; the left above is solved using coordinate motion (all pieces moving together at the same time), and the right above is solved by halving two halves that slide together. The hardest part is trying to visualize what it should look like together once it is apart. Here is what the two solutions look like when starting to come apart:
a.k.a. Triple Play
Purchased from Bits and Pieces 2007.
(wood, 3 inches)
Looks like three pieces but is actually a level 1 non-standard 6 piece burr (six pieces (three light wood and three dark wood pieces). Here is the solution that came with the puzzle:
Designed by F. Potts, made by E. Fuller 2008, purchased from Cubic Dissection.
(Walnut and Maple, 3 inches)
Six pieces with magnetic tips assemble to look like a three piece burr (e.g., Just The Three). The pieces are all identical; here are photos of different views of them:
Here are photos of pulling apart the whole assembly and an assembly of four:
The solution is almost as much of a dexterity puzzle as a logic puzzle, where there is only one way to put two together that will lead to a solution, then it is easy to spread them apart and put in the next two, then harder to spread apart the four to get in the fifth, and then after pushing everything back together, a bit tricky with only two hands to get in the sixth piece. Here is a photo of the assembly of four with the two remaining pieces still to be put in:
Designed by Gregory Benedetti, made by Eric Fuller 2011.
(Acrylic, Yellowheart, 2.25 inches)
Here is what the puzzle maker said about this puzzle in the sale listing:"Reminiscent of Padaung Rings, this nifty little pocket puzzle is a lot of fun to solve. With a level 14.4.2 it's tricky but not impossible ... once you get the correct alignment and piece selection, it flows fairly quickly."
Copyright ThinkFun 2010.
(plastic, 2.75 inches square)
Comes with a solution booklet that has 37 steps to disassemble reading forward and 37 steps to assemble by flipping over the booklet and reading in the other direction.
Further Reading
Booklet pages.
Designed (with a computer) by Bill Cutler and Frans de Vreugd 2001, level 13
(Hard Maple and Jatoba, 2.25 inches)
Two 1x4x6 pieces in each dimension. Making top dark wood and the bottom light wood makes the level 13 solution unique. The number of "holes" (internal voids) is 13 because the volume of assembled shape if it was solid is 104, and adding up the volume of the six pieces gives 91. Here are sheets that came with the puzzle (copyright by and courtesy of Bill Cutler).
Purchased from ThinkFun 2006.
(plastic, 6 pieces, 2.75 inches)
Made by D. Alsmeyer 2007, Sabriday Puzzles.
(6 different woods, 3.5 inches)
The booklet that comes with the retail plastic puzzle shows 65 steps to completely take the puzzle apart. McFarren's Page shows a solution that removes the first piece in 28 steps, and completely takes the puzzle apart in 35 steps.
Further reading:
McFarren's Page, from: http://www.geocities.com/abcmcfarren/math/gordian.htm
Sabriday's wood description (Mahogany, Maple, Cherry, Purpleheart, Walnut, Paduk).
Designed and made by Franz de Vreud 2003, unique level 16.
(Maple and Granadillo, 2.9 inches assembled)
a.k.a. Kumiki Puzzles
These were made in Japan and owned by J. A. Storer in the 1960's. The Cleverwood Page credits these simple types of burrs to Tsunetaro Yamanaka (born 1874) and his descendants; here is a diagram of a cube from the 1942 Filipiak book, and an inexpensive circa 2000 plastic ball:
Further Reading
Cleverwood Page, from: http://www.cleverwood.com/kumiki.htm
Directions That Came With The Ball
Designed by Junichi Yananose, made by Eric Fuller.
(7 wood pieces, 3 inches)
Looks at first like a standard 6-piece burr. However, one of the apparent pieces is really two pieces.
Made in Japan, circa 1930?, level 1, no holes.
(cardboard box, 2.6" x 2.1" x 7/16", 9 wood pieces, and solution sheet;
box cover similar to other vintage Japanese exports like the Yamato Puzzle;
this puzzle was also made in a 22-piece version)
Here are photos of basic solution steps:
Designed by P. McDermott, made by B. Young and P. McDermott,
purchased from Mr. Puzzle Australia in 2007, level 6.
(wood, 10 pieces, 3.25 by 6.25 by 2.5 inches)
Here are the directions and solution that were sold wih the puzzle:
Designed by Bill Cutler.
(wood, 3.5 inches, 11 pieces and 5 ball bearings)
Eleven pieces in a 2-4-5 configuration. Takes 5 balls (it came with 4 inside and you are asked to put the 5th in). Two are in a notch near the top of 11. The other three can be in a portion of the bottom part of piece 11 when it is pushed up, but in order to get 11 in place, they must be shaken out into other places that lock up the other pieces. Number the ends as follows:
Disassembly:1. Jiggle the balls if necessary and move 11 up. 2. Two balls are always in a notch near the top of 11; jiggle the other three so that they are in a cavity at the bottom of 11. 3. Slide 8 up (1 and 2 get dragged with it). 4. The balls will now all fall out. 5. Slide 5 out. 6. Slide 11 out. 7. Slide 3 and 10 out. 8. Remove 7 and 9. 9. Remove 4. 10. Remove 6. 11. 1, 2, and 8 now come apart.Assembly:1. Assemble the puzzle without the balls by reversing the disassembly. 2. Slide 11 and 8 up (8 gets 1 and 2 dragged with it). 3. Put the two balls in the top and then slide a pencil through the puzzle to keep them from coming out. Then turn the puzzle over and put the other three balls in. 4. Slide 8 down (dragging 1 and 2 with it) as you carefully remove your pencil. 5. Shake the three balls so they leave the bottom of 11; then slide 11 down.
a.k.a. Hexsticks, Notched Hexagonal Sticks
Patented by S. Coffin 1973, made by 3M 1970,
also discovered independently by B. Cutler.
(12 plastic pieces, 3.5 inches)
Three solutions for assembling the twelve notched sticks are described on pages 116-118 of Coffin's book. The package is shown above; it has the directions on the bottom (also shown above) and inside is a hexagonal shaped solution booklet. Below are two panels from each side (other three are shown on the next page):
Further Reading
Coffin Patent, from: www.uspto.gov - patent no. 3,721,448
Cutler's Hectix Page, from: http://home.comcast.net/~billcutler/stock/hectix.html
Cutler's Hectix Revisited Page, from: http://home.comcast.net/~billcutler/stock/revisited.html
S.S. Adams Co., 1961.
(12 plastic pieces, each 1.5 by 3/8 by 3/8 inches)
S.S. Adams Co., 1961.
(12 plastic pieces, each 1.5 by 3/8 by 3/8 inches)
Purchased from Bits and Pieces 2007.
(10 wood pieces with solution sheet, 4.5 inches;
shown as "The Mystery" on pages 107-108, 141-142 of the 1893 Hoffmann book)
Copyright 1991-2007 Junichi Yananose, purchased in Japan 2010.
(aluminum, 12 pieces, 3.5 inches square)
Here is the box and the text on the front and back:
The puzzle slides apart in two halves and a free piece:
Designed by Bill Cutler and made by Jerry McFarland 2003.
(Walnut, 12 pieces, 2 by 2 by 8 inches)
Here is the sheet that came with the puzzle (copyright by and courtesy of Bill Cutler):
Designed by Bill Cutler 1981.
(Maple / Walnut / Cherry, 3.7 inches, 12 pieces)
Designed by Bill Cutler 1982.
(Maple / Walnut / Cherry, 4 inches, 13 pieces)
Designed by B. Cutler in 1983, made by Mr. Puzzle Australia 2008, level 11.
(Queensland Silver Ash / Queensland Blackbean / Mackay Cedar, 14 pieces, 4";
sold with directions and solution shown above)
Designed by B. Cutler 1984, made by E. Fuller 2008.
(Maple / Walnut / Mahogany, 15 pieces, 4 inches)
Designed by Bill Cutler and made by Jerry McFarland 2000.
(wood, 3 inches, 13 pieces + 2 pins)
Looks like the Wausau '82 puzzle, but different inside; here are excerpts from the puzzle sheet (copyright by and courtesy of Bill Cutler):
- Position the puzzle on a table so the group of three are vertical and the group of six with the dot is facing you, with the dot on the right (upsidedown from the figure).
- Give the puzzle a hard spin clockwise to move the pins into their holes.
- Simultaneously, the center rod of the three goes up, the rod with the dot comes out toward you, and the rod to its left goes back away from you. You will see the pins in the ends of the rod with the dot and the one next to it (take them out so you don't lose them).
- Now the puzzle comes apart.
Designer unknown, made by Eric Fuller.
(Purpleheart / Maple / Lacewood, 13 pieces, 2.25 by 3 by 3.75 inches)
Here is what Eric Fuller says:"This 13 piece interlocking burr puzzle was published in the magazine Soumen Kuvalehti number 11 in 1926. There are 2 possible solutions, both very similar. Despite its not being a high level puzzle, the solution is surprisingly tricky, probably because of its unusual shape. Ishino Keiichiro posted it on his site and Matti Linkola discovered the magazine."
Level 1, circa early 1900's??
(4" wood box with directions and 18 wood pieces, 3.6 inches assembled;
right vertical piece in photo above is solid key piece.)
Designed by Bill Cutler 1975.
(Maple / Walnut / Cherry, 3.6 inches, 18 pieces)
Designed 1992 and made by Jerry McFarland, purchased from cubicdissection.com 2008.
(Walnut, Mahogany, Maple, 19 pieces, 3.5" by 2.6" high, 7/8 inch square sticks)
Disassembly involves manipulating the central 4 pieces like opening a lock.
Here is the diagram of the pieces from the solution sold with the puzzle and photos of removing three pieces:
Further Reading
Solution that was sold with the puzzle.
"Made in Japan K.K.", circa 1920's?
(20 wood pieces, 4 inches;
box cover similar to other vintage Japanese exports like the Yamato Puzzle)
Two pairs of identical 4" pieces, four identical 2.5" pieces, eight identical 1.3" pieces, and four identical 1.3 inch solid pieces assemble to a somewhat two-dimensional snowfake arrangement; here is a photo of the box and the solution sheet:
Purchased from Pentangle Puzzles 2007.
(wood, 7.5 inches, 20 pieces)
Made in Japan, circa 1930?, level 1, no holes.
(cardboard box, 4.1" x 3.4" x 1/2", 21 wood pieces, and solution sheet;
this puzzle was also made in a 9-Piece Version)
Designed by Bill Cutler and made by Jerry McFarland 2003, level 85.
(Cherry / Walnut, 21 Pieces, 3 by 3 by 3.6 inches)
The Binary Burr functions like the Chinese Rings puzzle:
There are six "ring" pieces that must be manipulated in order to remove the "bar" piece; the remaining 14 pieces don't move and form the "cage' that constrains the movements. It basically takes two moves for each move of the corresponding Chinese Rings puzzle.
Purchased from Interlocking Puzzles 2000.
(wood, 2.5 by 2.5 by 9.8 inches)
Four standard 6-piece burrs that share one dimension. Pieces 4, 8, and 10 are identical, pieces 1, 5, and 15 are identical, pieces 12 and 16 are identical, pieces 11 and 14 are identical, and pieces 9 and 13 are identical:
Designed by Wayne Daniel 1982, made by Interlocking Puzzles.
(wood, 4.8 inches)
a.k.a. Eight Burrs
Designed by David Bruce, made by Interlocking Puzzles 2000.
(wood, 24 pieces, 4.8 inches)
The basic idea is to combine two eight piece assemblies and then add eight "outer" pieces. Here are diagrams of the pieces from the solution that came with the puzzle:
Assembly A pieces:
Assembly B pieces:
Outer pieces pieces:
Further Reading
Lost Day solution that was sold with the puzzle (pdf 9 pages).
Purchased from Interlocking puzzles 2002.
(13 ply Baltic Birch rings 7.2", Australian Jarrah rods 2.25", 18 pieces)
Four 6-piece burrs connected in one dimension by a pair of rings. Requires multiple counter rotations of the rings to disassemble or assemble. Interlocking Puzzles said:
"The eight radial pieces have slightly angled notches and can be sorted into four right handed and four left handed pieces. The eight axial pieces have normal notches. The four unique higher level burrs are distinctly different. The lengths of the burr rods are greater than 6 units. If these were four stand alone burrs they would require five, four, or three moves to get the first piece out. One of them would also require three moves to get the second piece out. It is a fun challenge to assemble each individual burr onto the rings and then remove it before facing the larger challenge of the whole puzzle."
Purchased circa 2000.
(plastic, 2.25 inch cube with 3D cross)
Similar idea to the Two Piece Oddity, with a frame and a 3D cross like piece that has to be removed.
Designed by Tom Jolly, made by Eric Fuller circa 2000.
(T'Zalam, 3 inches)
A frame and a 3D cross like piece that has to be removed.
Designed by Stephane Chromine, made by Eric Fuller, 2011.
(Walnut and Yellowheart, 3" x 2.25" x 1.5") The top two pieces are identical. Different assemblies are possible depending on how the top two pieces are rotated. In their easiest positions, the bottom piece can be removed in 8 moves. However, in one configuration, 12 moves are required to remove the bottom piece (given a reasonable way of counting rotations). Below are 9 of the positions for disassembly starting with the top piece rotated as the puzzle was shipped. Although the middle piece starts in its correct rotation for the final steps of disassembly, after pulling out and tilting down the bottom piece, the middle piece is rotated and drops down to allow the top piece to be rotated, and then the middle piece can be pushed up and rotated back so that the top two pieces are together and up to allow the bottom piece to be removed. Note that it now takes only 8 steps to put the puzzle back together by leaving the top two pieces in their existing rotations.
Designed by Ramos & Abad, made by Pelikan 2006, level 13.
(wood, 2.4 inches)
a.k.a. Internal Combustion
Designed by Tado Muroi early 1990's.
(left: "Pandora's Box", Mr. Puzzle Australia, Queensland Blackbean, 3.5x3.5x2.25";
right: "Internal Combustion", Bits and Pieces, Aluminum, 2.25" x 2.25" x 1.5";
described in Boardman's book)
Four burr pieces (two of which are identical) in a frame. Below is a 9-step assembly (6 steps to remove the first piece) based on the piece orientations shown on the right above (except in the photo above the left two have been flipped upside-down for better viewing):
1.2.
2.
4.5.
6.
7.8.
9.
A 12-step assembly where the piece labeled 3 is reversed from the 9-step assembly shown on the preceding page:
A 15-step assembly (see also the Boardman book):
Purchased from Bits And Pieces, 2008.
(wood, 3.4 inches square assembled by 7/8 inches thick, with solution sheet)
Sold by Interlocking puzzles 2000.
(wood, 2.5 inches)
The only set of 6 notchable pieces that can be assembled into 6 different level 1, no-hole, standard six piece burrs. Here is the solution that was sold with the puzzle:
Designed and made by Jean-Claude Constantin, purchased used 2006.
(13 pieces, set is 6.25" x 3.25 x 2.5 inches, each piece is 3/4 x 3/4 x 3 inches)
A set of 13 pieces to make 40 different notchable 6 pice burrs; the same set of 6 is sometimes used for several different problems (pieces in different positions). Each piece is 2 by 2 by 8 units.
JCC's 40 Problems:
1. ADFIKL
2. ADFIKL
3. ABDKLM
4. ABDKLM
5. ABDKLM
6. ACDKLM
7. ACDKLM
8. ACDKLM09. ADGHKL
10. ADEJKL
11. AFGIKL
12. AFIJKL
13. AEGIKM
14. AFHJLM
15. ADHIKM
16. ADEFLM17. ACGKLM
18. ACGKLM
19. ACJKLM
20. ACJKLM
21. ABGKLM
22. ABGKLM
23. ABJKLM
24. ABJKLM25. ADEIKM
26. ADEIKM
27. ADFHLM
28. ADFHLM
29. AGHIKM
30. AGHIKM
31. AEFJLM
32. AEFJLM33. BCFIKL
34. BCFIKL
35. BEFHIM
36. BEFHIM
37. BEFHIM
38. BEFHIM
39. BEFHIM
40. BEFHIM
JCC's Solution Hints:
1. AK-LI-FD
2. AL-KF-DI
3. AM-IK-BD
4. AL-MK-BD
5. AK-ML-DB
6. AD-MC-KL
7. AD-KC-ML
8. AD-LC-KM09. AL-KH-GD
10. AK-LE-DJ
11. AK-GF-LI
12. AL-JI-FK
13. AK-GE-MI
14. AL-JH-FM
15. AD-IH-KM
16. AD-FE-ML17. AL-KC-GM
18. AM-KC-GL
19. AK-LC-MJ
20. AM-LC-KJ
21. AK-MG-BL
22. AK-LG-BM
23. AL-MJ-KB
24. AL-KJ-MB25. AK-ME-DI
26. AM-KE-DI
27. AL-MH-FD
28. AM-LH-FD
29. AM-IH-KG
30. AK-IH-MG
31. AM-FE-JM
32. AL-FE-JL33. BI-LC-FK
34. FB-CK-LI
35. BE-HF-MI
36. BH-EI-FM
37. FH-EM-BI
38. EI-MH-FB
39. EH-FM-BI
40. EH-MI-FB
Purchased from Creative Craft House 2007.
(wood box 3.4" x 9.25" x 4.1" with 27 wood pieces, each 3.1" long by 3/4" square)
This set has 27 2x2x6 unit standard 6-piece burr pieces numbered from 0 to 26, where piece 0 is the solid piece. A total of 69 different level 1 standard 6-piece burrs can be selected, where all use piece 0 as a key piece, and the other 5 pieces are specified with a tic-tac-toe notation:
Made by Interlocking Puzzles 2000.
(7 x 6 x 3.4 inch Jarrah box with 42 Chechen pieces, each 3/4 x 3/4 x 2.4 inches)
25 distinct notchable 2 x 2 x 6.5 unit pieces, indexed from A to Y, a total of 42 pieces including duplicates, which can be used to assemble the 314 different level 1 six piece burrs that have no holes. The set comes with five puzzle cards and five solution clue cards that list the pieces in order from 1 to 6 according to where they belong in the diagram above. This set does not contain all possible notchable pieces; just has the pieces necessary (and enough copies) to make all 6-piece notchable burrs with no holes. Also, some higher level burrs can be constructed with this set; for example, L5 Notchable is OODXNL and Holey Astigmatism is TYLLUM. Note that because the pieces are more than 6 units long, there are some higher level burrs that don't quite work, but would if the pieces were exactly 6 units long.
A
B
C
D
E
F
G
H
I
J
K
L
M
N
O
P
Q
R
S
T
U
V
W
X
Made by Interlocking Puzzles 2000.
(6.6 x 5.75 x 3.2 inch wood box with 42 wood pieces, each 3/4 x 3/4 x 2.25 inches)
35 distinct notchable 2 x 2 x 6 unit pieces, indexed with numbers in the range 0 to 56 (as shown above), a total of 42 pieces including duplicates, which can be used to assemble most of the level 5 standard 6-piece burrs. Uses David Winkler's numbering. Four puzzle and clue cards that list the pieces in order from A to F according to the diagram above.
00
01
02
03
04
05
06
07
08
09
10
19
20
21
22
23
24
25
26
28
29
30
32
33
34
35
38
39
40
44
45
46
49
53
56
Assembling a cube shape from pieces is so common it merits its own category. Most of these puzzles leave you with a bag of pieces when unassembled, but a few, such as Hinged Cubes and Kev's Cubes are manipulation puzzles where you can pick it up, play with it, and put it down unsolved to continue later.
Copyright 1966 Piet Hein,
produced in Denmark by Skj0de of Skjern for Parker brothers, No. 1050.
(4" box with wood pieces, metal base, and instruction booklet, 3.1" assembled)
Six of the 7 pieces are formed from 4 unit size cubes and the last piece isformed from 3 unit size cubes; the goal is to assemble them into a 3x3x3 cube. This is a relatively easy puzzle with many solutions. John Rausch credits the invention of this puzzle to Piet Hein in 1936.
Further reading:
Stewart Coffin's book, from: http://www.johnrausch.com/PuzzlingWorld/chap03a.htm
McFarren's Page, from: http://www.geocities.com/abcmcfarren/soma/soma.htm
Lagoon Solution, from: http://www.give-me-a-clue.com
Johnson 1988 Patent, from: www.uspto.gov - patent no. 4,784,392
Johnson 1989 Patent, from: www.uspto.gov - patent no. 4,844,466
Designed by Stuart Coffin circa 1975, made by Cubic Dissection 2002.
(6 pieces, bocote, 2.25 inches square assembled)
Here is what Coffin says in The Puzzling World of Polyhedral Dissections:
"The six-piece version of the 3 x 3 x 3 cube will be considered first. For aesthetic reasons, one might prefer that all the pieces be the same size, but this is impossible, so the nearest approximation is to use three four-block pieces and three five-block pieces. It is also desirable that all pieces be non-symmetrical but this is likewise impossible so two of the four-block pieces will have an axis of symmetry. All pieces will of course be dissimilar. Of the several thousand such combinations possible the author tried several that proved to have either multiple solutions or no solution, until finally finding one with a unique solution."
Here is the solution hint that was sold with the puzzle:
Designed and made by Interlocking Puzzles circa 2001.
(5 pieces, 3 inches square assembled)
A similar theme, but not the same set of pieces as the 5 piece version of the 3x3x3 cube suggested by Stewart Coffin in Figure 55 of The Puzzling World of Polyhedral Dissections.
Designed by Stuart Coffin (circa 1975), Made by Interlocking Puzzles (circa 2001)
(4 pieces, 3 inches square assembled)
The photo on the right above shows the four pieces in their relative orientation for assembly. Here is what Coffin says in The Puzzling World of Polyhedral Dissections:
"With puzzles of this type, there are an optimum number of pieces; and as you tinker with them, you soon gain an intuitive sense of what that number is. There is no way that a four-piece version can be very difficult, although the one shown in Fig. 51 does have the intriguing property of being serially interlocking, meaning that it can be assembled in one order only. Is a five-piece serially interlocking version possible?"
Made by AussieStuff Puzzles, purchased from Mr. Puzzle Australia, 2006.
(13 pieces, wood, 6 inches)
Thirteen pieces, each designed from unit cubes, are assembled into a 4x4x4 cube; can also be assembled into a 4 x 16 rectangle. Here is the solution that was sold with the puzzle:
Purchased from UK3, 2006.
Here is a photo of the other three sides:
Purchased from Creative Craft House 2007.
(wood, 3.1 inches)
Named because the designer's wife commented that it would take a century to solve; here are the first few steps of dissassembly:
Designed by Stewart Coffin circa 1975, made by Interlocking Puzzles 2001.
(8 pieces, maple and bloodwood, 2 inches square assembled)
The wood used to make this puzzle gives a clue to the solution with symmetric color shown above; the photos below show three basic steps to this solution:
It is not unique, here are two views of another solution:
Stewart Coffin, in his book The Puzzling World of Polyhedral Dissections, describes the derivation of this puzzle as starting with all possible pairs of joined 1x2x2 blocks (where the resulting 10 pieces can be assembled into a 4x4x5 solid in 25 different ways) and then eliminate the two rectangular pieces (the 1x2x4 piece and the 2x2x2 piece) to see if the remaining 8 pieces can be assembled into a cube. He then goes on to say that they cannot be so assembled, but that one can be eliminated and one duplicated to make a set that can. He also notes "an interesting pattern of symmetry" in the solution.
The 1986 patent of Guenther describes puzzles where pieces are formed from pairs of rectangular solids.
Further reading:
Guenther Patent, from: www.uspto.gov - patent no. 4,534,563
"Just a Little Packing Problem #1",
made by Mr. Puzzle Australia, purchased 2006;
basic idea by Stewart Coffin circa 1975.
(8 pieces, Tasmanian Oak, 2 inches square assembled)
Like the Stewart Coffin Patio Block, puzzle, but with a slightly different set of pieces. The three photos below show basic solution steps:
Designed by Bill Cutler 1991, made by Cutler / McFarland / Peterson.
(wood, 2.5 inches)
Pieces formed from black and white unit cubes and half unit cubes (starred above) must be assembled to a 3x3x3 cube with a checkerboard pattern on all sides. The solution is unique and does not follow the checkerboard pattern in the hidden center.
Designed by V. Genel, sold by Puzzleman.com, circa 2000?
(Zebrawood and Walnut, 2+5/8 inches)
Four beautifully cut pieces ome apart in pairs:
Designed by S. Coffin 1971, made by T. Lensch 2008.
(Marblewood and Brazilian Blackwood, 2.2 inches;
sold with a piece diagram piece diagram and an assembly diagram)
Described in Coffin's book, six identical pieces are augmented to make 6 different non-symmetric pieces, where two groups of three slide together diagonally:
Basic idea by Stewart Coffin, made by J. Storer 1989.
(purple heart with light wood dowels, 3 inches)
Stewart Coffin proposed this class of puzzle to make a 2x2x2 cube from 8 unit cubes, where each has three mutually perpendicular holes, and a total of 12 dowels are inserted into 12 of the 24 holes. He observed that the holes have one of two "reflexive forms", and that puzzles could be made by having all pieces of one form or having 4 with one and 4 with the other. The cubes of this puzzle all have the left form; the photos show basic solution steps:
Basic idea by Stewart Coffin, made by J. Storer 1989.
(top: purple heart with dowels, 3 inches;
bottom: rosewood with dowels, 2.25 inches)
Like the Cubes and Pegs puzzle, except here 4 pieces have one form and 4 the other (the pattern of pegs in the soluton to this puzzle is different from Coffin's Book Fig. 193):
Designed by Ronald Kint-Bruynseels, made by Eric Fuller 2007.
(walnut box and 9 cocobolo pieces with pegs, 2.5 inches)
Nine identical 3-unit L-shaped pieces with pegs added to assemble in a unique solution to a 3x3x3 cube. Here are basic solution steps:
Patented by Andy Turner, made by Eric Fuller 2010.
(Oak box 2.75" square by 2.1" high, Bubinga puzzle 2.2" square)
Don't read any further; have some fun first. This puzzle is quite hard until one sees the trick, and then it is almost impossible to forget how to solve it.
The two 1x2 pieces have double holes at one end that naturally entices one to use them, but in fact these two faces butt against each other in the unique solution (no pegs going between them), and then the puzzle solves easily. Here are four photos in sequence of assembly:
Designed Stewart Coffin, made byInterlocking Puzzles 2000.
(7 pieces, bloodwood and aluminum, 3 inches)
There are a total of 7 pieces; 2 pieces formed from 5 unit cubes with holes and rods, 4 pieces formed from 4 unit cubes with holes and rods, and one 3 unit long rod. They must be assembled into a 3x3x3 cube (there is a unit void in the center). Stewart Coffin proposed this class of puzzles and suggested this particular selection of pieces as one that has a "satisfactory" set of two solutions. Below are two stages of a solution for which the last piece placed before the rod is the T, and two stages of a solution for which the last piece placed before the rod is the Z:
Designed Stewart Coffin; left Interlocking Puzzles 2005, right Coffin circa 1980.
(left: mahogany, eight pieces, 3.25 inches,
right: mahogany, walnut, szjo, eight pieces, 2.75 inches;
right is one of 6 puzzles purchased during a visit to Coffin's house early 1980's)
Featured in a December 1991 article in Fine Woodworking Magazine. Described in Stewart Coffin's book The Puzzling World of Polyhedral Dissections; here is some of what he says in the directions that came with the puzzle:"Special version - only one made. No half-pieces, so ignore puzzle problems that require half-pieces. The cube has only one solution in which all sides have matched wood and grain symmetry."The pieces are the eight ways to glue together a basic U-shaped piece; below are the pieces of the Interlocking puzzle version, the one made by Coffin pulled apart, and Coffin's grain pattern:
The wood and grain restriction has only one solution, but on the other hand, you are given clues how to do it. For example, there is just enough walnut to go around (a total of 8 squares), and so the solution cannot have any of the walnut squares hidden in the middle. For the single wood version, here is one of the solutions:
For the single wood version, Interlocking Puzzles said that there are 7 solutions each with a symmetric version; here is the solution sheet that was sold with the puzzle:
Designed Rick Eason 2004, purchased from Mr. Puzzle Australia 2006.
(Burdekin Plum, 2.4 inches)
The solution is unique and made more difficult due to 3 "false solutions" (arrangements that could exist in a solved state but there is no order of assembly to achieve any of them). Below are photos of two steps in the solution and the sheet that came with the puzzle:
Further reading:
Winter Patent, from: www.uspto.gov - patent no. 6,241,248
Designed by John Devost, made by Rick Eason 2007.
(Bocote and Cherry, 4 pieces, 2.4 inches)
Four pieces formed from unit cubes and rods of dimensions 1/2 by 1/2 by 2.5 units.
The photos below show the four pieces positioned to be assembled, and pairs put together; the final step slides these two halves together to get the solved cube shown above.
Designed by Kevin Holmes and Rik Van Grol, made by Eric Fuller 2009.
(Peruvian Walnut and Spalted Oak, 2.7 inches)
A beautiful and fun puzzle; here are photos of assembly:
a.k.a. Magic Cube
Circa 2000.
(laminated cardboard with Andy Warhol art, 2.75 inches)
Unlike the Hinged Cubes puzzle, this puzzle is trivial to solve and is more of a toy than a puzzle. The cube shown above, can be unfolded in two different ways to form a 2 x 4 array, and then in both cases that 2 x 4 array can be folded lengthwise to form another 2 x 4 array:
Designed and made by Jim Storer; patent applied for 2009.
(Kingwood with brass hinges, 2.25 inches square assembled)
Fold the eight cubes into a larger 2x2x2 cube; there are 7 hinges:
Hinge 1 joins cube 2 to cube 1, on the front faces.
Hinge 2 joins cube 3 to cube 2, on the back face of 3 and the right face of 2.
Hinge 3 joins cube 4 to cube 3, on the top faces.
Hinge 4 joins cube 5 to cube 4, on the front faces.
Hinge 5 joins cube 6 to cube 5, on the left face of 6 and the right face of 5.
Hinge 6 joins cube 7 to cube 6, on the back face of 7 and the front face of 6.
Hinge 7 joins cube 8 to cube 6, on the top faces.
A fun but not too hard puzzle; when left on a coffee table, people often spend 30 minutes or so to solve it (about right for a coffee table audience). Not only is there something very satisfying about the solid feel of real hinges, but they also tend to suggest a straightforward folding one cube at a time, which inevitably leads to a position like the one shown on the right above.
a.k.a. Snake Cubes, Serpent Cubes, Cubra Cubes
Designed by Trench Puzzles circa 1985, made by Jim Storer 1988.
(bloodwood, 2.8 inches assembled)
Twenty seven cubes are threaded together with an elastic cord to form a "snake" that can be folded up by rotating adjacent cubes with respect to each other; the object is to form a 3 by 3 by 3 cube (where none of the elastic cord shows).
Many puzzles are possible by threading different patterns. If you imagine the cubes alternately colored red, black, red, ..., then the solved 3x3x3 cube will have red cubes at the corners and the face centers. The Kev pattern is has a unique solution where the snake ends are face centers.
Further reading:
Jaap's Page, from: http://www.jaapsch.net/puzzles/snakecube.htm
Mark Weston's Page, from: http://www.cs.uvic.ca/~mweston/snakes.html
Eryk Vershen's Page; from: http://cantaforda.com/cfcl/eryk/puzzles/chain_cube.html
Dreyer Patent, from: www.uspto.gov - patent no. 3,222,072
a.k.a. Snake Cubes, Serpent Cubes
Same idea as Kev's Snake Cubes, but a different pattern.
(2 inches square)
The Cubra Cubes are the same idea as Kev's Snake Cubes, but come in a number of different patterns; this is the first pattern shown on Mark Weston's Page:"A solution can be described by a string of "directions" that the cube follows when you wrap it into a cube, either Right, Left, Up, Down, Forward, or Back. So for example if a solution starts R R F L ... then put the end of the snake with the rest trailing off to the Right, then the next cube goes in the same direction (it must be a straight-through cube), the next cube (a corner cube) turns to point Forward, then it goes Left, etc."Unlike Kev's Cubes, a solution starts and ends in the corners, and is not unique. Here is a solution that is provided for the Lagoon version of this puzzle (the same as the first one above, with the directions R-L, F-B, U-D all reversed):
Solutions:
R R F L U U F D D R U B B L L F D F U U B B R R F F
R R U L F F U B B R F D D L L U B U F F D D R R U U"
Further reading:
Mark Weston's Page, from: http://www.cs.uvic.ca/~mweston/snakes.html
Lagoon Solution, from: http://www.give-me-a-clue.com
Packing puzzles typically require one to fit pieces into a tray (two dimensional) or a box (three dimensional), although sometimes the problem is to fit the pieces into a particular shape. Perhaps the most well known example, which as been around for centuries, is the tangram, where the goal is to use the same set of simple two dimensional shapes to make many different shapes.
a.k.a. All Square Novelty Puzzle, Check-A-Board, Tyr & Do It,
Famous Checkerboard Puzzle, Weekly Telegraph Chessboard Puzzle
Left: Made 1940's by a relative of J. A. Storer who lived in up-state New York.
(wood cigar box and painted pieces cut from 1/4" masonite, with 1" squares)
Right two: J. F. Friedel Co., Syracuse, N.Y, circa 1940's.
(6.5 by 8 by 1" cardboard box and 12 cardboard pieces with 1+3/8" squares;
top edge says "Mfg. by J. F. FREDEL CO. Syracuse N.Y.";
bottom edge says "MFGS. REPRESENTATIVES POTTER & REAGAN")
Arrange the pieces to make a standard 8 by 8 checkerboard. There are 10 distinct pieces and two of the 5-unit Z's. Shown on pages 70-73 of the Haubrich book, which lists a unique solution (shown above). Here is another version made in Great Britian:
All Square Novelty Puzzle, Frederick Warne & Co.,
London and NY, circa 1930's?
(6.25 x 6.25 x 13/16 inch cardboard box
and 12 wood pieces based on 15/16" squares 1/8 inch thick;
directions on the back of the box)
Note: Frederick Warne & Co. is the publisher of
the 1893 Hoffmann book.
Patented by H. Luers and made by Selchow & Righter, NY, circa 1880.
(8.5 inches square by 3/4 inch cardboard box and 15 cardboard pieces, 14 distinct;
pieces based on 1 inch squares can be arranged in the box;
on the cover and pages 217-219 of the Haubrich book,
which lists this puzzle having 6,013 solutions;
solution on the left above is from Haubrich, and right is from the Luers patent)
Left is a solution a previous owner drew inside the box bottom, right is the label on the box top, and below is the label inside the box top.
This version is nearly identical to the one shown on the previous pages, except the color of the label on the box top is a bit more brown than gray, and the pattern around the edge is a bit different (and this one has nothing inside the box top or bottom).
Phenyo-Caffein Co., Worcester, MA, circa 1900.
(5.25 inches square by 5/8 inch cardboard box and 15 cardboard pieces, 14 distinct;
pieces based on 5/8 inch squares can be arranged in the box;
also made with a wood box of the same dimensons and graphics)
The Pheno-Caffein Co. also made the Misfit 6 Piece Burr. The inside of the box bottom (on the right above) challenges the solver by stating that the dark square of the smallest piece can occupy any of the 32 dark squares. The sheet available from the company, on the next page, shows eight solutions (representing solution classes).
Further Reading
Luers Patent, from: www.uspto.gov - patent no. 231,963
a.k.a. Famous 'Bug House' Puzzle
Feltham Co., London, Royal Letters Patent 16,310, circa 1889.
(cardboard box and 14 thick cardboard pieces, 5" x 5" x 1/2";
box bottom has add for Feltham's tennis bat;
has a sheet that is the same as what is on the inside of the box bottom;
shown on pages 165-174 of the Haubrich book,
which gives the date and lists this puzzle as having 84 solutions; one is shown above)
Franco, NY, circa 1948.
(cardboard box and 14 distinct metal pieces, 3.25" x 3.25" x 1/2")
The Bug House Puzzle, E.I.H. Co. and F&K, 1912.
(cardboard box and 14 distinct metal pieces, 2.1 by 3.1 by 1/2 inches;
inside box top gives directions and manufacture;
shown on the cover and on pages 150-151 of the Haubrich book,
which gives the manufacture date,
identifies "E. I. Horsman Co." and "Forsheim & Koningsberg", NY,
and lists this puzzle as having 141 solutions, one of which is shown below)
Note: There were a number of variations of this puzzle made. This one is the same as page 150-151 of the Haubrich book if the pieces with dots in the photo above are taken to be black; however, the dots shown in the Haubrich book are not in the same locations.
Vasen Mfg. Co., Davenport, Iowa, 1928.
(cardboard box and 14 distinct cardboard pieces, 4.25 by 4.25 by 5/8 inches;
inside box bottom says you can send 10 cents to get three different solutions;
shown on pages 158-164 of the Haubrich book,
which lists this puzzle as having 84 solutions, one of which is shown above)
Note: Pages 165-174 of the Haubrich book show puzzles that are the same except for the colors reversed, and pages 183-187 of the Haubrich book include the same box top where if the pieces for those puzzles have the colors reversed, they are the same except for one (and the same as Xcel Checkerboard Puzzle No. 1).
Doyle Puzzle Co., Buffalo, NY, circa 1920?
(cardboard box 5.1"x5.1"x7/8", and 14 distinct cardboard pieces with 3/4" squares;
same as the Famous and Baffling Checkerboard Puzzle with colors reversed;
also made in a 13 piece version, the New XceL Checkerboard Puzzle No. 2;
shown on pages 183-187 of the Haubrich book,
which lists this puzzle as having 84 solutions, one of which is shown below)
Note: The Chequers Puzzle shown on page 97 of the 1893 Hoffmann Book is the same as a mirror image of this puzzle, except that puzzle shows only 63 squares, and can be corrected to make one of the three 4-unit L's be a 5-unit Z.
Doyle Puzzle Co., Buffalo, NY, circa 1920?
(cardboard box 5.1"x5.1"x7/8", and 13 distinct cardboard pieces with 3/4" squares;
also made in a 14 piece version, the XceL Checkerboard Puzzle No. 1;
shown on page 122 of the Haubrich book,
which lists this puzzle as having 7 solutions,
5 of which a composed of two 4 by 8 solutions,
one of these 5 and one other are shown below,
where the black squares correspond to green and the white to black)
Gyro Checker Board Jig Saw Puzzle, undated.
(3.5 by 6 inch envelope and 14 distinct cardboard pieces based on 1 inch squares;
shown on page 196 of the Haubrich book,
which lists this puzzle as having 598 solutions, one of which is shown below)
a.k.a. Krazee Checkerboard Puzzle, Zebas Puzzle,
Banzee Island Checkerboard Puzzle, 59-444 Checkerboard Puzzle
Peter Pan Playthings, England, circa 1950.
(plastic box and 12 plastic pieces, 4.75 by 4 by 5/16 inches;
there are 11 distinct pieces, where there are two of the 6-unit L;
shown on pages 57-65 of the Haubrich book, which gives the manufacture date
and list this puzzle as having 11 solutions, one of which is shown above;
pages 60-65 show reflected with reverse colors patented by J. Avila-Valdez 1995)
Arrange the pieces to make a standard 8 by 8 checkerboard. Paper, shown below, is glued to the bottom inside of the box that gives a layout for quickly storing the pieces unsolved in the box. The bottom of the box is a non-transparent black plastic that does not allow you to see the back of the paper. However, by holding it up to the light one can see that the reverse side of the paper has instructions similar to the Krazee Checkerboard Puzzle, shown on the following page.
Further Reading
Avila-Valdez Patent, from: www.uspto.gov - patent no. 5,403,005
Krazee Checkerboard Puzzle, Plas-Trix Co., Jamica, NY, 1957.
(plastic box and 12 plastic pieces, 4.75 by 4 by 5/16 inches;
same puzzle as the Draught Checkerboard Puzzle shown on the previous page,
but the back of the box is clear to allow one to view directions;
also shown on pages 57-58 of the Haubrich book, which gives the manufacture date)
Zebas Checkerboard Puzzle, Plas-Trix Co., Brooklyn, NY.
(plastic box and 12 plastic pieces, 4.75 by 4 by 5/16 inches;
same puzzle as the Krazee Checkerboard Puzzle shown on the previous page,
and also made by the Plas-Trix Co., but with different packaging)
Banzee Island Checkerboard Puzzle, made in Hong Kong.
(12 plastic pieces in plastic bag with cardboard top, 6.25 by 6.5 inches;
same puzzle as the Zebas Checkerboard Puzzle shown above,
the back of the package top refers to Chief Zebas)
S. Adams Co. Neptune, NJ., Copyright 1958.
(6" by 4" cardboard package and six 3.5 by 2.5 inch puzzles,
the checkerboard and five others, including Magic T;
shown on page 167 of the Adams Co. History book;
shown on page 21 of the Haubrich book.
which presents the unique solution shown above)
Made in Japan circa 1940.
(wood box 3.8 by 3.75 by 7/16 inches thick and 19 wood pieces;
wood inlays on the box cover are 5/8 inch diameter;
paper stamp on the back is 1/2 inch square)
Purchased from someone who remembered it from his childhood in the 1940's. At some point in the past the following solution was drawn:
This puzzle has the same dimensions, style, and cover inlays as the 16 piece puzzle on page 233 of the Haubrich book. However, even if one assumes that the 1x1 pieces broke off of larger ones before the solution above was drawn, and taking into account rotations and reflections (the pieces are double sided), there is no way to make it the same (and no way to further combine pieces to make it the same as the 14 piece puzzle of the same style on page 177) Here are the 16 pieces if the 1x1's are joined to the pieces above them in the solution above:
a.k.a. Caricature, Cut-Up Square, Stone Tangram,
Union Stone Puzzle, Richter Anchor Stone Puzzle No. 8
F. AD. Richter, Rudolstadt, Nurnberg, Olten, Wein, NY, circa 1890's / early 1900's.
(cardboard box 3.1" x 3.1" x 9/16", 7 stone pieces, booklet, and solution booklet;
"casse tete" and "kopfzerbrecher" mean headache in French and German;
described on pages 77-79, 96-97, 111-115, 128 of the 1893 Hoffmann book.
inside of the cover shows how to pack the pieces into the box;
inside of the box bottom has an add for "Dr. Richter's Pain-Expeller";
booklet has multi-language text inside covers and on pages A to Q at the front,
and 64 pages with 195 shapes to make,
where the last 16 pages are shapes made in combination with another puzzle;
second booklet has solutions)
An old design known as the Tangram, dating back to ancient China; seven tiles, called Tans, can be used to make different shapes. The Richter Company of Germany, known for stone building blocks, started making this puzzle and others in 1891. It is number 8 of over 36; see The Tangram Book, The Anchor Puzzle Book, Slocum and Botermans books, and also the Richter Summary later in these pages. Many versions of the tangram have been made, some packaged as two squares of half the area:
Richter (1846-1910) had a number of business besides stone building sets and puzzles, including selling medicines (see the Richter history on the Ankerstein Page). Many of the Richter puzzles have adds or testimonials to his pain medicine. The add below is on the inside of the box bottom of the puzzle on the preceding page.
The text on pages A to Q at the start of the booklet that precedes the 64 pages of shapes is very similar to that in versions of a number of other Richter puzzles (e.g., see the corresponding pages for the Tormentor and Pythagoras puzzles). Page L describes how the last 16 pages are shapes made in combination with another puzzle; shapes 180 to 183 use the Circular Puzzle, shapes 184 to 187 use the Tormentor, shapes 188 to 191 use the Cross Puzzle, and shapes 192 to 195 use Pythagoras. An English description similar to what is on Page L is given in the description that came with the "Puzzle Drive" version shown below.
Note: These pages are shown in order (left to right, top to bottom), except that page 64 (pattern 195) is shown with page 1 (patterns 1 through 4).
Richter Co., circa 1890's / early 1900's.
(cardboard box 3.2 by 3.2 by 5/8 inches, 7 stone pieces, and two booklets;
the inside of the cover shows how to pack the pieces into the box;
box is constructed with a lip on the bottom,
booklet cover says "The Anchor Puzzle 3rd Ed",
booklet inside cover for "Casse-Tete Persan" and cover for "Kopfzerbrecher",
which says that this is the "third edition" at a price of "15 kr.",
is followed by a 3 page French and German introduction,
followed by unnumbered pages of shapes similar to the puzzle on the first page,
followed by a final page, in German, that advertizes Anchor blocks
by referring to the picture on the back of the booklet;
second booklet is a work book with shapes to draw in and many blank pages)
Richter Co., circa 1890's / early 1900's.
(cardboard box 3 by 3 by 9/16 inches, 7 stone pieces, and two booklets;
similar to the version on the previous page;
a more compact box where the small bottom lip is hidden when the cover is on;
box top graphics and booklet front and back (shown above) are the same;
inside box bottom advertizes "ANCHOR PAIN EXPELLER" from 1890;
booklet is basically the same except it is in German and English;
booklet inside cover for for "Kopfzerbrecher" and "The Anchor Puzzle",
which says that this is the "third edition" at a price of "10 cents",
followed by a 3 page German and English introduction,
followed by unnumbered pages of shapes similar to the puzzle on the first page,
folloed by a final page, in English, that advertizes Anchor blocks
by refering to the picture on the back of the booklet)
Richter Co., circa 1890's / early 1900's.
(cardboard box 3.1 by 3.1 by 1/2 inches, 7 stone pieces, and booklet;
the inside of the cover shows how to pack the pieces into the box;
box bottom lists other puzzles for sale,
the booklet has 64 pages of the same 195 shapes as the puzzle on the first page,
along with the single loose double sided page of English directions shown above)
some versions have the same box cover with "UNION" instead of "ANCHOR"
and the same booklet cover with just "STONE PUZZLE" on a single line)
Richter & Co., Germany, copyright 1917.
(cardboard box 3.1 by 3.1 by 5/8 inches, 7 stone pieces, and booklet;
the inside of the cover shows how to pack the pieces into the box;
box and booklet front show copyright, and booklet back shows the U.S. manufacturer;
the booklet has text on the insides of the covers and 48 pages
of the same 179 shapes as the first 48 pages of shapes on the first page;
unlike earlier versions of this puzzle, an explicit copyright date is shown)
Richter & Co., Germany, circa 1890's / early 1900's.
(cardboard box 3.1 by 3.1 by 9/16 inches, 7 stone pieces, and booklet;
the inside of the cover shows how to pack the pieces into the box;
the booklet has 64 pages of the same 195 shapes as the puzzle on the first page,
however its cover is blank, and there is no text explaining that
the last 16 pages are shapes made in combination with another puzzle;
the pages of this booklet were used for the scans shown earlier)
a.k.a. All Nine, Richter Anchor Stone Puzzle No. 1
Richter & Co., Germany, circa 1890's / early 1900's.
(cardboard box 2.7" x 4.4" x 1/2", 9 stone pieces, and booklet;
similar in construction to the Anchor Puzzle Tangram;
the inside of the cover shows how to pack the pieces into the box;
booklet has multi-language text inside the covers and on pages A to Q at the front,
and 48 pages with 141 shapes to make,
the first of which is the star, which can be solved as shown above,
and where the last 16 pages are shapes made in combination with another puzzle)
Richter & Co., Germany, circa 1890's / early 1900's.
(cardboard box 2.7" x 4.4" x 1/2", 9 stone pieces, and booklet;
booklet has the same shape pages as the one on the previous page,
but no additional text pages;
back of the box lists other puzzles)
a.k.a. Richter Anchor Stone Puzzle No. 2
Richter & Co., Germany, circa 1890's / early 1900's.
(cardboard box 3.1" x 3.6" x 9/16", 7 stone pieces, and booklet;
similar in construction to the Anchor Puzzle Tangram;
the inside of the cover shows how to pack the pieces into the box;
booklet has multi-language text inside the covers and on pages A to Q at the front,
and 48 pages with 140 shapes to make;
where the last 16 pages are shapes made in combination with another puzzle;
the first four shapes are the rectangle, parallogram, triangle, and hexagon)
Same size box and booklet as version on the preceding page.
The booklet starts with 16 not numbered pages, where the first 12 are a page of directions in 12 different languages, and the last 4 pages have multi-language text with a coupon that could be mailed in along with 15 cents to get solutions to all of the problems. Following these 16 pages are 48 pages of the same problems as the version on the preceding page. The booklet front cover, inside of the front cover, inside of the back cover, and the back, present the same text in 12 different languages; on the inside of the back cover, the English text says "Second book to The "Lightning Conductor" for drawing in the lines of solved problems." So it would appear to be the second of two booklets that originally came with the puzzle.
Same size box and booklet as version on the preceding pages.
The booklet has 48 pages of the same problems as the version on the preceding pages.
(same pieces but different shapes than Richter 16 Magic Egg)
a.k.a. a.k.a. Columbus' Egg, Columbian Puzzle, Richter Anchor Stone Puzzle No. 3
Richter & Co., Germany, circa 1890's / early 1900's.
(cardboard box 3.1" x 4.1" x 9/16" with wood inserts, 9 stone pieces, and booklet;
similar in construction to the Anchor Puzzle Tangram;
the inside of the cover shows how to pack the pieces into the box;
the booklet has multi-language text inside the covers and on pages A to Q at the front,
and 48 pages with 111 shapes to make,
where the last 16 pages are shapes made in combination with another puzzle;
there are no graphics on the back of the booklet)
Richter & Co., Germany, circa 1890's / early 1900's.
(cardboard box 3.1" x 4.1" x 1/2" with wood inserts, 9 stone pieces, and booklet;
the inside of the cover shows how to pack the pieces into the box;
the booklet has multi-language text inside the covers and on pages A to Q at the front,
and 32 pages with 95 shapes to make;
the booklet is the same as the one on the preceding page
except without the final 16 pages)
a.k.a. Richter Anchor Stone Puzzle No. 4
Richter & Co., Germany, circa 1890's / early 1900's.
(cardboard box 4.1" x 3.1" x 9/16", 8 stone pieces, and booklet;
similar in construction to the Anchor Puzzle Tangram;
the inside of the cover shows how to pack the pieces into the box;
booklet has multi-language text inside the covers and on pages A to Q at the front,
and 48 pages with 130 shapes to make,
where the the directions state that the first is the square using only 6 pieces,
the second is the right triangle of 3/2 the height of the square using only 7 pieces,
all others use all eight pieces,
and where the last 16 pages are shapes made in combination with another puzzle)
Richter & Co., Germany, circa 1890's / early 1900's.
(cardboard box 3.1" x 4.1" x 1/2", 8 stone pieces, and booklet;
similar booklet with the same shapes as the version on the previous page)
a.k.a. Richter Anchor Stone Puzzle No. 5
Richter & Co., Germany, circa 1890's / early 1900's.
(cardboard box 3" x 3.6" x 9/16", 7 stone pieces, and booklet;
similar in construction to the Anchor Puzzle Tangram;
the inside of the cover shows how to pack the pieces into the box;
booklet has multi-language text inside the covers and on pages A to Q at the front,
and 48 pages with 108 shapes to make,
where the last 16 pages are shapes made in combination with another puzzle)
Richter & Co., Germany, circa 1890's / early 1900's.
(cardboard box 3" x 3.6" x 9/16", 7 stone pieces, and booklet;
the inside of the cover shows how to pack the pieces into the box;
booklet has multi-language text on pages A to Q at the front,
and 48 pages with the same 108 shapes to make as the puzzle on the preceding page)--- 201 --- Trouble Killer, Continued
Richter & Co., Germany, circa 1890's / early 1900's.
(cardboard box 3" x 3.6" x 9/16", 7 stone pieces, and booklet;
the inside of the cover shows how to pack the pieces into the box;
this one is missing the booklet;
it came with some extra cardboard pieces
that are in the bottom of the box below the stone pieces)
a.k.a. Richter Anchor Stone Puzzle No. 6
Richter & Co., Germany, circa 1890's / early 1900's.
(cardboard box 3.5" x 3.5" x 9/16", 9 stone pieces, and booklet;
similar in construction to the Anchor Puzzle Tangram;
the inside of the cover shows how to pack the pieces into the box;
booklet has multi-language text inside the covers and on pages A to Q at the front,
and 32 pages with 98 shapes to make;
the text above is on the box bottom under the puzzle)
Richter & Co., Germany, circa 1890's / early 1900's.
(cardboard box 3.5" x 3.5" x 9/16", 9 stone pieces, and booklet;
booklet has the same 32 pages with 98 shapes to make
as the puzzle of the previous page, but no additional text;
included is one loose double sided page of text)
a.k.a. Goblin, Richter Anchor Stone Puzzle No. 7
Richter & Co., Germany, circa 1890's / early 1900's.
(cardboard box 3" x 4" x 9/16", 7 stone pieces, and booklet;
similar in construction to the Anchor Puzzle Tangram;
the inside of the cover shows how to pack the pieces into the box;
booklet has multi-language text inside the covers and on pages A to Q at the front,
and 48 pages with 143 shapes to make;
where the last 16 pages are shapes made in combination with another puzzle;
a previous owner has penceled in a solution to the first problem shown above)
a.k.a. Richter Anchor Stone Puzzle No. 9
Richter & Co., Germany, circa 1890's / early 1900's.
(cardboard box 3.6" x 3.6" x 9/16", 10 stone pieces, and booklet;
described on pages 85-87, 120-121 of the 1893 Hoffmann book;
similar in construction to the Anchor Puzzle Tangram;
the inside of the cover shows how to pack the pieces into the box;
booklet has multi-language text inside the covers and on pages A to Q at the front,
and 48 pages with 121 shapes to make;
where the last 16 pages are shapes made in combination with another puzzle)
Richter & Co., Germany, circa 1890's / early 1900's.
(cardboard box 3.6" x 3.6" x 9/16", 10 stone pieces, and booklet;
the inside of the cover shows how to pack the pieces into the box;
the booklet starts with 8 pages of multi-language text,
followed by 48 pages of the same 121 shapes as the puzzle on the first page;
this box top was made with a number of variations a b of the text for different markets)
Richter Co., circa 1890's / early 1900's.
(cardboard box 3.7" x 3.7" x 9/16", 10 stone pieces, and booklet;
the inside of the cover shows how to pack the pieces into the box;
box bottom lists other puzzles for sale,
booklet has 48 pages of the same 121 shapes as the puzzle on the first page,
along with the single loose double sided page of English directions shown above)
a.k.a. Sherlock Holmes, Hi Ho, Richter Anchor Stone Puzzle No. 10
Richter & Co., Germany, circa 1890's / early 1900's.
(cardboard box 3" x 3.75" x 9/16", 7 stone pieces, and two booklets;
described on page 83-85, 118-119 of the Hoffmann book;
similar in construction to the Anchor Puzzle Tangram;
the inside of the cover shows how to pack the pieces into the box;
the inside of the bottom has a testimonial dated 1899,
variations of this testimonial appear in the box top or bottom other versions;
first booklet has multi-language text inside covers and on pages A to Q at the front,
and 48 pages with 149 shapes to make
the first of which is the cross as shown above,
and where the last 16 pages are shapes made in combination with another puzzle;
the second booklet gives a solution for each shape)
Same dimensions as version on the first page;
the inside of the cover shows how to pack the pieces into the box;
booklet has nothing on the inside covers,
with 8 unnumbered pages of multi-language text,
followed by the same 48 pages of problems as the version on the first page;
the first page credits Dr. Richter's Publishing House, 215 Pearl St., NY;
second booklet is the same solution booklet as the one on the first page.
Same dimensions as version on the first page;
box construction uses a lip on the bottom;
the inside of the cover shows how to pack the pieces into the box;
inside of the bottom has a testimonial dated 1890;
inside covers and first 8 unnumbered pages have multi-language text,
followed by 48 pages with the same problems as the version on the first page;
however, the problems are drawn with black line art rather than red coloring;
the first page of problems is shown to the right of the booklet cover above;
second booklet has solutions for problems on the first 32 pages.
Note: Version shown on the top right is Dutch version; it says "Kruisraadsel" at the bottom of the box top and on the front cover of the booklet (which has the identical pages).
Same puzzle as the one shown on the first page;
3" x 3.7" x 1/2";
booklet has the same 48 shapes to make,
but without the text pages at the front and back.
a.k.a. Richter Anchor Stone Puzzle No. 11
Richter & Co., Germany, circa 1890's / early 1900's.
(cardboard box 3.1" x 3.1" x 5/8", 8 stone pieces, and booklet;
similar in construction to the Anchor Puzzle Tangram;
the inside of the cover shows how to pack the pieces into the box;
booklet has 8 pages of multi-language text at the beginning,
and 32 pages with 89 shapes to make)
Richter & Co., Germany, circa 1890's / early 1900's.
(cardboard box 3.1" x 3.1" x 9/16", 8 stone pieces,
the inside of the cover shows how to pack the pieces into the box;
booklet has multi-language text inside covers and on pages A to Q at the front,
and 32 pages with 89 shapes to make, same as those on the preceding page)
Richter & Co., Germany, circa 1890's / early 1900's.
(cardboard box 3.1" x 3.1" x 5/8", 8 stone pieces,
and booklet of 32 pages with the same 89 shapes as the preceding page)
a.k.a. a.k.a. Richter Anchor Stone Puzzle No. 12
Dr. Richter's Publishing House, 215 Pearl St., NY, circa 1890's / early 1900's
(cardboard box 3 by 3 by 9/16 inches, 8 stone pieces, and booklet;
described on pages 81-83, 117-118 of the 1893 Hoffmann book;
similar in construction to the Anchor Puzzle Tangram;
the inside of the cover shows how to pack the pieces into the box;
the inside of the bottom has a testimonial dated 1899;
booklet has multi-language text inside the covers and on pages A to Q at the front,
and 64 pages of 197 shapes to make,
where the last 16 pages are shapes made in combination with another puzzle)
Described on page L of the booklet, the last 16 pages are shapes made in combination with another puzzle; shapes 182 to 185 use the Anchor Puzzle, shapes 186 to 189 use the Tormentor, shapes 190 to 193 use the Circular Puzzle, and shapes 194 to 197 use the Cross Puzzle.
Note: These pages are shown in order (left to right, top to bottom), except that page 64 (pattern 197) is shown with page 1 (patterns 1 through 3).
Here are the front and back cover, the inside front cover, pages A through Q that come before the problem pages, and the inside back cover. The text in German, French, and English discusses this and other puzzles, and gives testimony from a satisfied customer.
Similar to the version on the first page, but
box has different construction with a lip on the bottom,
booklet has multi-language text on inside covers and 6 unnumbered pages,
and the booklet has the same problems but drawn with black and white art
(first three pages of problems shown above)
Richter & Co., Germany, circa 1890's / early 1900's.
(cardboard box 3 by 3 by 1/2 inches, 8 stone pieces, and booklet;
the cover slides on;
the inside of the bottom shows how to pack the pieces into the box;
the booklet is 48 pages of 181 puzzles;
these 48 pages are the same as the first 48 pages of the puzzle on the first page;
there is an extra double-sided text page in German between pages 18 and 19,
that seems to be a bit out of place because it discusses
the combinations that would be on the other 16 pages)
a.k.a. Richter Anchor Stone Puzzle 13
Dr. Richter's Publishing House, 215 Pearl St., NY, circa 1890's / early 1900's.
(cardboard box 3 by 3 by 9/16 inches, 8 stone pieces, and booklet;
described on pages 80-81 of the 1893 Hoffmann book;
similar in construction to the Anchor Puzzle Tangram;
the inside of the cover shows how to pack the pieces into the box;
the inside of the bottom has a testimonial dated 1899;
booklet has multi-language text inside the covers and on pages A to Q at the front,
and 64 pages with 174 shapes to make,
where the last 16 pages are shapes made in combination with another puzzle)
Described on page L of the booklet, the last 16 pages are shapes made in combination with another puzzle; shapes 159 to 162 use the Circular Puzzle, shapes 163 to 166 use the Anchor Puzzle, shapes 167 to 170 use the Cross Puzzle, and shapes 171 to 174 use Pythagoras.
Note: These pages are shown in order (left to right, top to bottom), except that page 64 (pattern 174) is shown with page 1 (patterns 1 through 4).
Here are the front and back cover, the inside front cover, pages A through Q that come before the problem pages, and the inside back cover. The text in German, French, and English discusses this and other puzzles, and gives testimony from a satisfied customer.
Same as the version on the first page
except for the art on the box top and the front and back of the booklet
(same box top inside, testimonial, booklet text and problems).
Similar to the version above, but
box has different construction with a lip on the bottom,
booklet has multi-language text on inside covers and 8 unnumbered pages,
and the booklet has the same problems but drawn with black and white art
(first three pages of problems shown above)
a.k.a. Richter Anchor Stone Puzzle No. 14 (sometimes 3)
Richter & Co., Germany, circa 1890's / early 1900's.
(cardboard box 3" x 3+7/8" x 1/2", 10 stone pieces, and booklet;
similar in construction to the Anchor Puzzle Tangram;
the inside of the cover shows how to pack the pieces into the box;
the booklet has 48 pages with 136 shapes to make,
where the last 16 pages are shapes made in combination with another puzzle;
the solution to the first problem in the booklet is shown above)
Note: Although usually referred to with the number 14, some versions of the box graphics showed the number 3.
a.k.a. Richter Anchor Stone Puzzle No. 14 /3
Richter & Co., Germany, circa 1890's / early 1900's.
(cardboard box 3" x 3+78" x 1/2", 10 stone pieces, and booklet;
the inside of the cover shows how to pack the pieces into the box;
booklet has 48 pages with the same 136 shapes to make as the preceding page)
a.k.a. Lott's Stone Puzzle, Anchor Puzzle No. 15 (sometimes 16)
Richter & Co., Germany, circa 1890's / early 1900's.
(cardboard box 2.7" x 4.4" x 9/16", 7 stone pieces, and booklet;
similar in construction to the Anchor Puzzle Tangram;
the inside of the cover shows how to pack the pieces into the box;
a second way of packing the pieces into the box is shown by the figure above;
the inside of the bottom has a testimonial dated 1899;
booklet has multi-language text inside the covers and on pages A to Q at the front,
and 48 pages with 135 shapes to make,
the first of which is the pyramid of square root 3 times the height of the rectangle,
and where the last 16 pages are shapes made in combination with another puzzle;
Note: The box above does not show a number. However this puzzle was commonly listed by in Richter literature as number 15, and 15 appears on the boxes of some versions. It was also made with a box that has the same graphics as the one above with "No. 16." above the word Sphinx.
Puzzle pieces the same as the first page but box is 2.75" x 4.9" x 1/2";
booklet has the same 48 pages of problems but no additional text;
the inside of the cover shows how to pack the pieces into the box;
directions are on a separate two sided sheet that is slightly smaller than booklet pages.
"Lott's Stone Puzzle", copyright 1911, Lott's Bricks, LTD, Watford, England.
(cardboard box 2.7" x 4.2" x 9/16", 7 stone pieces, and booklet;
the booklet pages 1 and 2 are an introduction,
the last page invites one to write for a solution to another puzzle,
and pages 3 through 31 show 105 shapes to make,
where page 31 shows the rectangle for how to pack the pieces into the box)
(same pieces but different shapes than Richter 3 Egg Of Columbus)
a.k.a. Miracle Egg, Richter Anchor Stone Puzzle No. 16 (sometimes 17)
Richter & Co., Germany, circa 1890's / early 1900's.
(cardboard box 3.1" x 4.1" x 9/16" with wood inserts, 9 stone pieces, and booklet;
booklet has 48 pages with the same 106 shapes to make
as the puzzle on the following page, but without the other pages of text)
Richter & Co., Germany, circa 1890's / early 1900's.
(cardboard box 3.1" x 4.1" x 9/16" with wood inserts, 9 stone pieces, and booklet;
also made with the similar box top but without "No. 17",
the inside of the cover shows how to pack the pieces into the box;
the booklet has multi-language text inside the covers and on pages A to Y at the front,
and 48 pages with the same 106 shapes to make as puzzle in preceding page;
the first page of shapes has written "Copyright Nachdruck verboten";
all shapes use only the 9 pieces of the puzzle;
the booklet names each shape in pages A to Y)
a.k.a. Richter Anchor Puzzle No. 17
Richter & Co., Germany, circa 1890's / early 1900's.
(cardboard box 3.5" x 3.5" x 9/16", 7 stone pieces, and booklet;
similar in construction to the Anchor Puzzle Tangram;
the inside of the cover shows how to pack the pieces into the box;
booklet has multi-language text inside the covers and on pages A to Q at the front,
and 48 pages with 113 shapes to make,
where the last 16 pages are shapes made in combination with another puzzle)
Richter & Co., Germany, circa 1890's / early 1900's.
(cardboard box 3.5" x 3.5" x 9/16", 7 stone pieces, and booklet;
the inside of the cover shows how to pack the pieces into the box;
booklet has multi-language text on eight unumbered pages at the front,
and 48 pages with the same 113 shapes to make as the puzzle on the previous page,
where the last 16 pages are shapes made in combination with another puzzle;
this Gnome theme box top was made with different variations of the text)
Richter & Co., Germany, circa 1890's / early 1900's.
(cardboard box 3.5" x 3.5" x 9/16", 7 stone pieces, and booklet;
the inside of the cover shows how to pack the pieces into the box;
the booklet has the same 48 pages with 113 shapes to make
as the puzzle on the first page, but with no additional directions)
Richter & Co., Germany, circa early 1900's.
(cardboard box 3.2" x 4.3" x 9/16", 9 stone pieces, and booklet;
similar in construction to the Anchor Puzzle Tangram;
the inside of the cover shows how to pack the pieces into the box;
booklet has multi-language text inside covers and on pages I to XIX at front,
where none of the text is in English,
followed by a blank page where a previous owner has drawn
a solution to the additional shape shown above,
followed by 32 pages with 97 shapes to make)
Richter & Co., Germany, circa early 1900's.
(cardboard box 2.25" x 4.25" x 1/2", 7 stone pieces, and booklet;
similar in construction to the Anchor Puzzle Tangram;
the inside of the cover shows how to pack the pieces into the box;
the booklet has English text on the inside of the covers shown above,
and 32 pages with 99 shapes to make,
where the first is the rectangle for the box packing
and next three are the parallelogram, square, and triangle shown above)
Richter & Co., Germany, circa early 1900's.
(cardboard box 2.75" x 3.7" x 1/2", 8 stone pieces, and booklet;
similar in construction to the Anchor Puzzle Tangram;
the inside of the cover shows how to pack the pieces into the box;
the booklet has English text on the inside of the covers shown above,
and 32 pages with 98 shapes to make,
where the first is the rectangle for the box packing
and the second is the parallelogram shown above)
Richter & Co., Germany, circa early 1900's.
(cardboard box 2.75" x 3.7" x 1/2", 8 stone pieces, and booklet;
similar in construction to the Anchor Puzzle Tangram;
the inside of the cover shows how to pack the pieces into the box;
the booklet has English text on the inside of the covers shown above,
and 32 pages with 98 shapes to make,
where the first is the rectangle for the box packing
and the second is the parallelogram shown above)
Richter & Co., Germany, circa early 1900's.
(cardboard box 2.75" x 3.7" x 1/2", 9 stone pieces, and booklet;
similar in construction to the Anchor Puzzle Tangram;
the inside of the cover shows how to pack the pieces into the box;
the booklet has English text on the inside of the covers shown above,
and 32 pages with 96 shapes to make,
where the first is the rectangle for the box packing
and the second is the octagon shown above)
Richter & Co., Germany, circa early 1900's.
(cardboard box 3.1" x 3.75" x 1/2", 8 stone pieces, and booklet;
similar in construction to the Anchor Puzzle Tangram;
the inside of the cover shows how to pack the pieces into the box;
the booklet has English text on the inside of the covers shown above,
and 32 pages with 96 shapes to make,
where the first is the rectangle for the box packing
and the second is the shape shown above;
label across front is from F. A. O. Swartz, N.Y.)
The manufacture for the Richter Anchor Puzzles began in the 1890's, where the puzzles numbered above 17 were made in the World War II era. The 1893 Hoffmann book describes the Anchor, Circular, Cross, Pythagoras, and Tormentor puzzles (and also the Star Puzzle). A history of the Richter puzzles is presented in The Anchor Puzzle Book by Jerry Slocum (see also the Slocum and Botermans books). The puzzle boxes were made with a variety of cover art (see the following page), although the stone pieces, made with the Richter Co. patented process, are the same. Perhaps what made these puzzles so popular were the fun booklets that came with them, giving a host of shapes to make.
Here is a booklet that came with the Anchor Puzzle, and also a corresponding solution booklet that one could purchase by mail:
Generally, booklets have more or less the same cover art as the box top, but not always. For example, on the left and middle are booklets for versions of the Tormentor and Cross Puzzle that look very different from the corresponding box top, and on the right is a booklet for a version of the Anchor Puzzle that has blank covers (and nothing inside besides the problem figures):
Here are two examples of additional work booklets that came with the Anchor and Lightning Conductor puzzles:
Some box themes were highly regular; here are some examples (the last one is used on boxes numbered above 17, the others for 17 and below):
Other themes used fun graphics (e.g., people thinking, specialized graphics, cartoons); here are some examples (all used on puzzles numbered 17 and below):
Richter 1
"The Nine"
Richter 2
"Lightning Conductor"
Richter 3
"Egg Of Columbus"
Richter 4
"Patience Prover"
Richter 5
"Trouble Killer"
Richter 6
"Heart Puzzle"
Richter 7
"Kobold"
Richter 8
"Anchor Puzzle"
Richter 9
"Circular Puzzle"
Richter 10
"Cross Puzzle"
Richter 11
"Not Too Hasty"
Richter 12
"Pythagoras"
Richter 13
"Tormentor"
Richter 14
"Be Quiet"
Richter 15
"Sphinx"
Richter 16
"Magic Egg"
Richter 17
"Wrath Breaker"
Richter 18
"Archimedes"
Richter 19
"Ende Gut, Alles Gut"
Richter 20
"Pass Auf"
Richter 21
"Eile mit Weile"
Richter 22
"Sorenbrecher"
Richter 23
"Kopernikus"
Richter 24
"Pyramide"
Richter 25
"Nur Mut"
Richter 26
"Bose Siben"
Richter 27
"Ritze Ratze"
Richter 28
"Frisch Gewagt"
Richter 29
"Zeitvertreiber"
Richter 30
"Zeppelin"
Richter 31
"Kiebitz-Ei"
Richter 32
"Wer Wegt Gewinnt"
Richter 33
"Fur Kluge Leute"
Richter 34
"Hexenmeister"
Richter 35
"Teufeldien"
Richter 36
"Heureka"
Here are pages from an old Richter Brochure (courtesy of Jerry Slocum, Puzzles Old And New, Copyright 1986, page 28); see also The Anchor Puzzle Book by Jerry Slocum.
Here (and on the following page) are the shapes used to make the 36 Richter Anchor Puzzles (courtesy of Jerry Slocum, Puzzles Old And New, Copyright 1986, page 28); see also The Anchor Puzzle Book by Jerry Slocum.
(second half of the figure from Puzzles Old And New, Copyright 1986, page 28)
Anker Page, from: http://www.ankerstein.org
Richter History, from: http://www.ankerstein.org/html/CO.HTM
Wikipedia Tangram Page, from: http://en.wikipedia.org/wiki/Tangram
Rubiks.com Double Tangram booklet, from: http://www.rubiks.com/World/Rubiks%20downloads.aspx
Rob's Tangram Page, from: http://home.comcast.net/~stegmann/tangram.htm
Slocum Database, from: http://webapp1.dlib.indiana.edu/images/search.htm?scope=lilly/slocum
a.k.a. Richter Picco Nr. T1
Richter & Co., Germany, circa early 1900's.
(cardboard box 2.125" x 2.125" x 3/8", 8 stone pieces, and problem sheet;
puzzle tray slides into the right side of the box with a small table to pull it out;
same pieces in a smaller size as Richter 13 Tormentor;
problem sheet has 26 shapes, where problem 11 shows how to pack into the box)
The first of three miniture Richter puzzles referred to as Picco or Piccolo (Nr. T2 is the same as Richter 12 Pythagoras; and Nr. T3 is the same as Richter 8 Anchor Puzzle; with the parallelogram piece divided into two triangles); see the Anchor Puzzle Book.
Further Reading
Indianna Slocum Archive (photos of Picco versions of Nr. T1 Nr. T2 a b c, Nr. T3 a b) from:http://webapp1.dlib.indiana.edu/images/search.htm?scope=lilly/slocum
RichterCo., circa 1890's / early 1900's.
(cardboard box 3.75" x 3.75" x 1/2", 48 stone pieces, and booklet;
16 white right triangles, 8 white wedges, 8 black wedges, 16 black quadralaterals;
described on pages 87-90, 122-124 of the 1893 Hoffmann Book;
inside of the cover shows how to pack the pieces into the box;
inside of the box bottom has an add for "Dr. Richter's Pain-Expeller";
booklet has multi-language text inside covers and on pages A to Q at the front,
and 48 pages with 153 shapes to make)
Like Meteor One, more of a two-dimensional building set than a puzzle. Other examples of unnumbered Richter puzzles include Blumen Spiel and Schutzengraben / Zoologischer Garten (same pieces but the Schutzengraben shapes are different than the Zoologischer Garten shapes); see the Anchor Puzzle Book.
Further Reading
Rob's Puzzle Page, from: http://robspuzzlepage.com/tangram.htm
Indianna Slocum Archive (including photos of Blumen Spiel BlumenSpiel and Schutzengraben a b c from:http://webapp1.dlib.indiana.edu/images/search.htm?scope=lilly/slocum
--- 251 --- Star Puzzle, Continued
RichterCo., circa 1890's / early 1900's.
(cardboard box 3.75" x 3.75" x 9/16", 48 stone pieces, and booklet;
inside of the cover shows how to pack the pieces into the box;
booklet has multi-language text inside covers and 8 not numbered pages at the front,
and 32 pages with 103 shapes to make,
which are the same 103 shapes as the 103 of the preceding page;
this puzzle has had 3 of the 4 sides of the box lid replaced,
4 missing white pieces replaced with pieces made from painted maple,
and three missing black pieces replaced with pieces made from Ebony)
F. AD. Richter, Rudolstadt Germany, New York, circa 1890's / early 1900's.
(cardboard box 6.3 by 6.3 by 5/7 inches, 4 colors marbles, and booklet;
more of a game than a puzzle, the object is to arrange the marbles into patterns;
in Richter's Puzzles and Pastimes catalog - see Anchor Puzzle references)
F. AD. Richter, Rudolstadt Germany, New York, circa 1890's / early 1900's.
(wood box 8.75" x 8.75" x 2.5", 6 colors marbles, and booklet;
like Meteor 1, arrange the marbles into patterns;
also includes a Nine Mens Morris, board;
in Richter's Puzzles and Pastimes catalog - see Anchor Puzzle references)
"Wm. F. Drueke & Sons, Grand Rapids, Mich.", circa 1940?
(cardboard box 2.5 by 5.75 by 13/16 inch thick, and 7 wood pieces;
assembles to a 4.1 inch square by 5/16 inches thick)
Tryne Games Mfg. Inc., Lindenhurst, NY, copyright 1961.
(cardboard box 5.6 by 9 by 7/8 inch thick, booklet, and 7 plastic pieces;
assembles to a 5.4 inch square by 3/16 inches thick;
the problems in the booklet are similar to the Richter 8 Anchor Puzzle booklet; this puzzle should not be confused with Richter 12 Pythagoras)
(Same pieces as Richter No. 10 Cross Puzzle)
Kogner Bros. Inc., Tryne Game Division, East Paterson, N.J., circa 1960's.
(cardboard box 5.6" x 9" x 13/16" with plastic tray, booklet, and 7 plastic pieces;
assembles to a 5.4 inch square by 3/16 inches thick;
the problems in the booklet are similar to the Richter 10 Cross Puzzle booklet;
the box and booklet are not dated,
but the booklet references a copyright 1961 version of the Tangram that it calls "Pythagoras")
(Same pieces as Richter No. 10 Cross Puzzle)
Hi Ho Puzzle, 1932.
(2.75 by 2.5 by 5/8 inch cardboard box, 7 plastic pieces, and directions)
The pieces are made from Bakelite (an old type of plastic developed in the early 1900's). Below are the top and bottom edges of the box and one of the sides (the other side is the same). The directions show a sitting dog and suggest that many other patterns can be made.
Further Reading
Wilipedia Bakelite Page, from: http://en.wikipedia.org/wiki/Bakelite
(Same pieces as Richter No. 10 Cross Puzzle)
Sherlock Holmes Puzzle, circa 1960.
(2.9" x 3.6" x 7/16" plastic box, 7 plastic pieces, and directions)
(Same pieces as Richter No. 3 and Richter No. 16)
Scrambled Egg, Copyright ThinkFun 2002.
(9 metal pieces in plastic tray, 4 by 3.5 by 5/16 inches;
puzzle comes with clear plastic sleeve for storage;
booklet slides into tray bottom, and presents problems with solutions shown above)
Carrom Co., Ludington, Michigan, circa 1920s?
(cardboard box and 7 wood pieces, 3.6 inches square by 9/16 inches thick)
Like the Anchor Puzzle Tangram, the directions that were sold with this puzzle give a host of patterns to make from seven pieces similar to those of the Tangram.
ELZZUP Puzzle Co., Keene, N.H., circa 1900.
(3.3" x 3.3" x 3/4" wood box and 10 wood pieces)
This puzzle was sold in 2011 by a person who said it had been owned by Eleanor Dows of Laurel Mass., the sister of his grandfather, who was born in 1890. The back of the box top has her name in pencil, and her name and the town of Laurel Mass. is burned into the box bottom. The arrangment of the pieces into a square is not unique. In the spirit of the Anchor Puzzle Tangram, the goal is to make fun patterns with the pieces.
Wm. F. Drueke & Sons, Grand Rapids, MI, circa 1940's - 1960's.
(top: cardboard box 3.2"x3.2"x1/2", problem booklet, and 10 wood pieces;
middle: plastic box 8"x8"x1.2", problem & solution booklets, 10 wood pieces;
bottom: cardboard box 7.5"x7.5"x3/4", problem & solution booklets, 10 wood pieces)
In the same theme as the Anchor Puzzle Tangram, all three of these versions present 57 pages of 200 shapes to make. The first version above has only a problem booklet, which also includes English, French, and Spanish pages at the beginning that indicate that the puzzle may be purchased by mail for 50 cents, and that a solution booklet can be ordered for 25 cents; the back of this booklet shows how to pack the pieces into the box.
(from the 8x8" version)
(from the 8x8" version)
Rockford Pattern Works, circa 1930's?
(4.25" square by 5/8" thick box, 9 wood pieces, and 4" square booklet)
The pieces are a square and four pairs of right triangles, where the sides of the smallest ones are the same as the sides of the square, and the hypotenuse of a larger one is twice the side of a next smaller one. Like the Anchor Puzzle Tangram, a booklet shows shapes to make. The last page gives solutions for four of these problems (only 7 of the nine pieces are shown for one of them). Here are the booklet pages (page 1 and the last page are shown together):
Further Reading
King Tut Wikipedia Page, from: http://en.wikipedia.org/wiki/King_tut
Rockford Foundries History, from: www.rockfordfoundries.com/about.cfm
German text on the package promotes Vision 2000; purchased 2010.
(cardboard box and four 7/16" thick wood pieces, 9.25" x 1.8" by 9/16")
In the theme of the Anchor Puzzle Tangram, using the same four pieces as the Missing T puzzle, the booklet gives 100 shapes to make, the first how to pack into the box and the last is the T:
Further Reading
Vision 2000 Page, from: http://www.vision2020.org/main.cfm
Copyright ThinkFun 2008.
(plastic, 5" x 5" x 1.4")
In the theme of the Anchor Puzzle Tangram, 14 pieces can be arranged into many shapes. The box has a tray that slides out with 60 problem cards of shapes to make (that give hints and solutions on the back).
Further Reading
Problem card backs.
Magic Square, circa 1960?
(plastic box 2.5 by 1.75 by 1/2 inches and 4 plastic pieces;
assembles to a 2.5 inch square)
a.k.a. Square Me, Five Block Puzzle, Madagascar Madness
ThinkFun Binary Arts, 2003.
(plastic, 4-piece square is 3 inches, solved 5-piece square is 3.2 inches square)
People often quickly find the four piece solution and then get stuck trying "stretch" the puzzle just a little bit in a way that will accommodate an additional small square piece. If the four piece solution is 4 units square, it has area 16, the extra square has area 2, and the five piece solution has area 18 (forming a square that is just under 4.25 units square); for each of the pieces in the four piece solution, its orientation is 45 degrees counter-clockwise in the five piece solution:
Characterized on page 102 of the 1942 Filipiak book Filipiak book as "recorded in the records of antiquity", has been periodically made as a promotional item.
CSPI promotional circa 1975.
(plastic, solved 5-piece 2.9 inches square;
this was a company that J. A. Storer's father was a part of in the 1970's;
came with a wire loop which J. A. Storer replaced in 2007 with Snowbird key ring)
"Madagascar Madness", Behavioral Sciences Inc., 1969.
(5 inches square by 3/4 inch thick plastic box and five plastic pieces;
the square piece was lost and replaced with a green plexi-glass piece)
This puzzle is packaged with a tray for the 4-piece solution and the 5th piece loose; perhaps to guide the solvers thinking away from the 5-piece solution. The directions on a 4.5 inch square card inserted into the back give an interesting discussion of the geometry:
Further reading
Dickinson's Witch Hazel promotional, unknown age.
(3" x 4.5" envelope with cardboard pieces, solved 5-piece square is 4" square;
Dickinson's Witch Hazel was first made in 1866 and was still being made in 2000)
Five Block Puzzle, S.S. Adams Co. circa 1950?
(1/4 inch thick wood pieces, solved 5-piece square is 5 inches square)
Dickinson's Witch hazel Page, from: http://www.witchhazel.com
Dickinson Co. Records, from:
http://www.lib.uconn.edu/online/research/speclib/ASC/findaids/
EEDickinson/MSS19960001.html
a.k.a. T Puzzle, Magic T, Cut-Up T, Pa's T Puzzle
Old design, copyright 1898 Lash Inc., this copyright ThinkFun Binary Arts 2003.
(plastic, 4 pieces, 3.1" high by 3" wide when solved)
The four pieces can be positioned to form a T as shown above. The HIQU puzzle has a booklet of problems based on these pieces. This is an old puzzle that has been produced many times; here is a nice antique wood one:
Pa's T Puzzle, circa 1940?
(cardboard box 4.6 by 1.75 by 11/16 inches and 4 walnut pieces,
5" high by 4.75" wide when solved;
box edge says "PA'S T PUZZLE No. P 20 WM. F. DRUEKE & SONS Grand Rapide, Mich.")
Circa 1960?
(plastic box 2.5 by 1.75 by 1/2 inches and 4 plastic pieces)
Made in Hong Kong, circa 1960?
(5.5 by 7 inch cardboard card with plastic pieces)
S. S. Adams Co., undated.
(3.5" cardboard sleeve with cardboard directions and dark green plastic pieces)
Designed by T. Linden, made by E. Fuller, 2009.
(velour bag and 7 English Brown Oak pieces, 3 inches assembled)
There are two 1x1x3 unit pieces each with one 45 degree pointed tip, three 1x1x2 unit pieces each with one 45 degree pointed tip, and two unit triangles.
By cheating just a little bit, an upper case H can also be formed. On the left below the upper right tip of the H is missing a unit triangle. In the middle, the pieces have all been rotated 90 degrees and are arranged so that the H looks perfect from above (it is formed from two 3 unit pieces on the left, two triangles for the cross, and three 2 unit pieces on the right, where there is a missing triangle on the top right tip when viewed from the side). On right below, again the pieces have all been rotated 90 degrees and are arranged so that the H looks perfect from above (it is formed from a 2 and 3 unit piece on each side, a 2 unit piece and a triangle for the cross, and the remaining triangle filling in one of the tips, with the other three tips having a missing unit triangle when viewed from the side).
Promotional puzzle from Mr. Puzzle Australia, 2008.
(6 thin flexible plastic pieces)
Made by interlocking Puzzles 2000.
(directions card and 6 identical Zebrawood pieces, each 2.25 inches)
Here is what Interlocking Puzzles said:"There are at least eighteen different challenges requiring the special angles and three, four, five, or six pieces of our Make a Square puzzle. Geometric shapes possible include triangles, squares, rectangles, pentagons, hexagons, parallelograms, and trapezoids. This tiling puzzle seems simple, but it is quite challenging to find all the solutions. These 6 pieces are each over 2 inches long, which allows the largest finished shape to be over 7 inches across the diagonal."
a.k.a. Endless Chain
Plas-Trix Co., Jamica, NY, circa 1957.
(plastic box and 14 plastic pieces, 4.75 by 4 by 5/16 inches;
same size / shape box as the Krazee Checkerboard Puzzle that is shown
on pages 57-58 of the Haubrich book, which gives the manufacture date; a puzzle like this is shown as the "Endless Chain" on page 99 of the 1893 Hoffmann book)
Plas-Trix Co., Jamica, NY, circa late 1950's
(plastic box and 12 plastic pieces, 4.75 by 4 by 5/16 inches)
Made by the same company and packaged like the Krazee Checkerboard Puzzle and the Krazee Links, but easier. Here are the packing instructions on the back of the directions and a solution:
Purchased 2004.
(wood base with metal pins, 7 wood pieces, 5 inches)
A board with metal pins must have 7 wood pieces (with holes) placed on it to form a square. The solution is not unique.
Designed by E. Nagata, copyright Binary Arts 2002.
(plastic and metal, 3.5 by 4.5 by 3/8 inches thick)
The puzzle comes with the pencils placed on one side of the board as shown above. The challenge is to flip the board over and pack them into the other side:
Designed by Bill Cutler, made by Walt Hoppe, and purchased 2006.
(15 pieces including the pearl and shell, 4.5 inches)
The goal is to place the thirteen wedge shaped pieces and the pearl (the little round piece) into the shell. After achieving the configuration shown above, the pearl is off to the right in the keeper hole, the pieces meet at a point in the center, and there appears to be no extra space. Now for the fun; the pieces can all be flipped over and space made to place the pearl in the center of the shell:
Designed by Bill Cutler and made by Walt and Chris Hoppe, 2008.
(25 wood pieces, each 3/16 inch thick, solved puzzle is 6.5 inch diameter circle)
Pack the 25 pieces to form a circle; here is what the directions say:"These pieces can be used to tile the plane non-periodically. They are a variation of the Penrose "Kites and Darts" tiles. Each barn is equivalent to the Penrose "Dart" piece, and the silos and tractors are each one-half of a "Kite" piece."The graphics on the 25 pieces are:(5) barn with a siloFurther Reading
(5) barn with a double silo
(5) barn (no silo) with a tractor
(5) barn (no silo) with a tractor towing a cart
(3) barn with a double silo and tractor
(2) barn with a silo and tractor towing a cart
Note: The directions say that some puzzles were made with the quanties 3 and 2 reversed.
Wikipedia Penrose Tiling Page, from: http://en.wikipedia.org/wiki/Penrose_tiling
a.k.a. Polyominoes
Old puzzle, this one made by Yasumi, 1995.
(wood, box and 12 pieces based on 0.75" inch cubes)
The 12 distinct shapes formed from 5 connected squares are the pentominoes (called polyominoes by Solomon W. Golomb, Charles Scribner's Sons, NY, 1965):
Total area is 60, and sizes 6 x 10, 5 x 12, 4 x 15, and 3 x 20 can be formed. There are known to be 2,339 distinct ways to form a 6 x 10 rectangle, excluding rotations and reflections. In contrast, there are 1,010 solutions for 5x12, 368 solutions for 4x15, and 3 x 20 has a unique solution except for rotating a central portion by 180 degrees.
A piece is landlocked if it does not touch one of the borders of the rectangle. Eric Harshbarger has determined that there are no 6x10 rectangle solutions with 5 or more landlocked pieces, but there can be solutions with 0, 1, 2, 3, or 4 landlocked pieces (e.g., there are 207 solutions of the 6x10 rectangle with four landlocked pieces, 1,111 with three, 864 with 2, 155 with one, and only a couple with zero).
R. M. Robinson of the University of California at Berkeley proposed the "triplication problem": Given a pentomino, use 9 of the other pentominoes to construct a scale model, 3 times as wide and 3 times as high as the given piece (all 12 are possible).
Pentominoes are traditionally flat pieces that can be arranged to form 2-dimensional patterns. However, if the pieces are made to be 1-unit thick, then fun 3-dimensional patterns can also be made, including a 3 x 4 x 5 solid, and stairs that are 6 wide by 4 deep by 4 high.
(The shaded area of the 3x20 solution may be rotated by 180 degrees.)
From the directions sold with the Yasumi version:
From the directions sold with the Interlocking Puzzles version:
Made By B. Cutler, 1989.
(3.25"x4"x2.375" plastic box and 12 two-color wood pieces with 3/4" cubes)
Can be used like any other pentominoes set. In addition, it is made from light and dark woods so that it can be solved in a 3x4x5 box where colors have a checkerboard pattern on all sides. Here is the diagram of the pieces from the directions that came with the puzzle:
Sold with this puzzle was printout of a number of solutions. Here is the one suggested; the pieces have the names 1, 2, 3, 4, 5, 6, 7, 8, 9, A, B, C, and this figure shows the three planes of the checkerbox:ABB5C A666C A636C
BB555 A7778 3333C
B9958 A9778 9944C
11111 22228 44428
From the directions sold with the Yasumi version:
Shown on Nivasch's Page:
Further Reading
Harshbarger's Page, from: http://www.ericharshbarger.org/pentominoes
Mathworld Page, from: http://mathworld.wolfram.com/Pentomino.html
CIMT Page, from: http://www.cimt.plymouth.ac.uk/resources/puzzles/pentoes/pentoint.htm
Gerard's Page, from: http://www.xs4all.nl/~gp/pentomino.html
Huttlin's Page, from: http://members.aol.com/huttlin/pentominoes.html
Nivasch's Page, from: http://yucs.org/~gnivasch/pentomino
Mark's Page, from: http://www.users.bigpond.com/themichells/packing_pentominoes.htm
Jankok's Page, from: http://homepages.cwi.nl/~jankok/etc/Polyomino.html
info Page, from: http://www.theory.csc.uvic.ca/~cos/inf/misc/PentInfo.html
Gottfriedville Page, from: http://www.gottfriedville.net/puzzles/colorgame/solutions.htm
Belgium Pentominoe page, from: http://home.scarlet.be/~demeod/indexe.html
Puzzle Will Be Played page, from: http://www.asahi-net.or.jp/~rh5k-isn/Puzzle
Fletcher's Page, from: http://www.andrews.edu/~calkins/math/pentos.htm
Wikipedia Page, from: http://en.wikipedia.org/wiki/Pentomino
Negahban Design Patent, from: www.uspto.gov - patent no. 385,311
Further reading about some related puzzles:
Lester Patent, from: www.uspto.gov - patent no. 1,290,761
Wadsworth Patent, from: www.uspto.gov - patent no. 3,964,749
Sarkar Patent, from: www.uspto.gov - patent no. 5,544,882
Designed by P. F. Ramos 2004, made by Interlocking Puzzles.
(wood frame and 12 pieces, 3.75" x 3.75" x 3" inches)
Standard pentominoes are the 12 different planar shapes that can be formed from 5 squares. There are 17 non-planar pentomino shapes (each made from 5 cubes). Here, 12 of them (which can be can be grouped into 6 mirror image pairs) must be packed into a 4x5x5 box frame; 40 units are used by the frame, leaving exactly 60 units of space to pack these pieces:
According to the sheet that came with the puzzle there are 54,189 possible ways these pieces can fit (in the sense that you could build the box around them), of which 23,549 of them can be achieved by starting with the box frame and inserting and moving pieces. Here is the layer by layer representation of the solution that came with the puzzle (X is the box):
A
B
C
D
E
F
G
H
I
J
K
LIn the orientations shown in the figures above, pieces can be inserted as follows:
top layer:
XXXXX
XJAFX
XJJFX
XCCFX
XXXXX2nd layer:
XGAIX
GGAFF
GJAAK
HJCDK
XDDDX3rd layer:
XGBIX
BBBII
EEELL
HHCKK
XDCKXbottom layer:
XXXXX
XBEIX
XHELX
XHLLX
XXXXX
1. B from behind.
2. I from behind.
3. G from behind.
4. E from below.5. H from below.
6. A from behind.
7. L from the right.
8. K from the front.9. F from behind.
10. C from above.
11. J from the top.
12. D from the front.
a.k.a. Sneaky Squares, Stark Raving Cubes, Block Out, Square Fit, KUBI
Designed by Bill Cutler, wood version made by J. Devost, 1983.
(left: oak, 4.5 inches square by 2.25 inches high;
middle: Sneaky Squares / Start Raving Cubes, plastic, 4.5" square by 2" high;
right: Block Out / Square Fit, 3" square by 1.25" high)
Four pieces cut at odd angles (so that they not quite cubes) must be placed into the box (a three piece version has also been made). Inserting one at a time will not work. To solve, arrange them on the table so that the top is level and square, push them together at the bottoms, and drop them into the box. Here is what the pieces look like in their solved positions, outside the box:
a.k.a. The Third Degree
Designed by Bill Cutler, made by W. Hoppe, 1995.
(wood, 3.75 inches by 1.75 inches high)
Three pieces that are cut at odd angles (so that they not quite the same) must be placed into the box. Like the larger Block Head puzzle, putting them in one at a time will not work; to solve, first arrange them on the table so that the top surface is level and a hexagon, and then push them together at the bottoms and drop them into the box. Here is what the pieces look like in their solved positions, outside the box:
Elverson Puzzle, 2002.
(wood box and 13 wood rods, 2.75 by 7.5 by 1.75 inches)
Pack 13 wood rods into the box. Here are th directions on the bottom of the box:
Here is the solved top layer taken out, showing the solved bottom layer in the box:
Made in the U.K., circa 2000?
(wood box and 18 wood rods, 2.7" square, with recessed silver dot stickers)
Pack the 18 rods into the box. A solution of 6 layers going from top to bottom is shown here from upper left to lower right (note that the rods of the top layer shown in the upper left all need to be rotated 180 degrees, as does the first rod in the second layer):
Designed by John Conway, copyright ThinkFun Binary Arts 2003.
(plastic, box and 9 pieces, 1.75" solved)
Also known as Conway's Curious Cube, and described on pages 736-737 of the Winning Ways books. Three unit cubes and six 1x2x2 pieces must be placed in a 3x3x3 box. In the unique solution, the three unit cubes line up diagionally through the cube from a corner to the center to the opposite corner:
Here is the solution that was sold with the puzzle:
Designer unknown, made by and computer analysis done by Bill Cutler 1979.
(wood box and 18 wood pieces, 4.8" by 6.8" by 1.7" thick)
A box of inside dimensions 18 x 28 x 6 units into which must be placed 18 two unit thick pieces of sizes 4x9, (2) 5x9, 5x18, 5x21, 6x7, 6x10, 6x13, (2) 7x8, (2) 7x13, 7x18, 8x18, 9x11, 9x13, 10x11, and 11x11. Cutler's analysis showed four solutions (not counting rotations and reflections), all placing the 4x9, 6x7, and 6x13 pieces on end. Here is one of them, from the sheets that came with the puzzle (copyright by and courtesy of Bill Cutler).
top layer middle layer bottom layer
Exchanging the middle and bottom layers gives a second solution, and these two solutions each have an alternate version by exchanging the 7x18, 5x21, 6x10 pieces on the top layer with the 7x13, 5x18, 10x11 pieces on the middle layer.
Designed by Bill Cutler with a computer 1992, made by Tom Lensch 2004.
(Wenge box with Bubinga pieces, 5 inches)
Here are the layers of the unique solution, from the sheet that was sold with the puzzle (copyright by and courtesy of Bill Cutler):
A host of puzzles have been made that require the solver to match adjacent edges or faces based on colors or patterns. Perhaps the most famous example of this type of puzzle is Instant Insanity, where one must line up four colored cubes so that each side has all four colors.
a.k.a. Rubik's Mini Tangle
Circa 1990, this one by J. A. Storer 2007 from a Rubik's Tangle 5x5.
(nine 2" cardboard squares in a 2.75 by 4 by 3/4 inch plastic box)
Arrange 9 squares in a 3x3 array so that edges match. Each square has the same pattern of 4 tangled ropes that has two connections on each edge. Different squares have a different combination of the four colors (red, green, blue, and yellow).
Jaap's Page indicates that this puzzle may have been produced as a give-away to promote the Rubik's Tangle 5x5 puzzle. The puzzle pictured here was made by using squares from a Rubik's Tangle 5x5. It's solution is the upper left 3x3 portion of the first solution to Version 1:
Further reading:
Jaap's Page, from: http://www.jaapsch.net/puzzles
Thurston Patent, from: www.uspto.gov - patent no. 487,798
Rankin Patent, from: www.uspto.gov - patent no. 606,338
Produced in 1995.
(nine 2" square plastic pieces, patterns on both sides)
Arrange 9 squares in a 3x3 array so that edges match. Each square has on both sides the same pattern of 4 tangled ropes that has two connections on each edge. Different sides of different squares have a different combination of the four colors (red, green, blue, and yellow). More confusing than Rubik's Tangle 3x3 because one has to decide how to flip the pieces.
Further reading:
Jaap's Page, from: http://www.jaapsch.net/puzzles/tangle.htm
McFarren's Page, from: http://www.geocities.com/abcmcfarren/math/r90/tangle.htm
Thurston Patent, from: www.uspto.gov - patent no. 487,798
Rubik's Tangle 1, 2, 3, and 4, Matchbox 1990.
(Box and twenty seven 2 inch cardboard squares.)
Arrange 25 squares in a 5x5 array so that edges match. Each square has the same pattern of 4 tangled ropes that has two connections on each edge. There is one square for each of the 24 possible combinations of the 4 colors (red, green, blue, and yellow), and one duplicate square. The only difference between Rubik's Tangle 5x5 Versions 1, 2, 3, and 4 is which piece is duplicated. By taking three pieces from a spare set, a single set of 28 squares can be made where three of the duplicates are left out to make one of the 4 puzzles. Below is a set made by starting with a Version 3 and adding three squares taken from a Version 2; the four duplicate squares have been labeled with a number on the back.
Further reading:
Jaap's Page, from: http://www.jaapsch.net/puzzles/tangle.htm
Thurston Patent, from: www.uspto.gov - patent no. 487,798
Rankin Patent, from: www.uspto.gov - patent no. 606,338
Price, Stern, Sloan Inc., Los Angeles, CA; Pig and Frog 1989, Train 1991.
(3.25 by 5.4 by 5/8 inch cardboard box and nine 3 inch cardboard pieces)
Like Rubik's Tangle 3x3, the directions on the back ask you to arrange the nine squares in a 3 by 3 array so that adjacent edges match; the Crazy Train directions state that there are exactly two solutions and are written in both English and Spanish.
Milton Bradley 1984.
(cardboard box and 12 plastic pieces, 7 by 5 by 1.5 inches;
"Lost Rope" is a translation of "Faden Verloren" that is written on the box.)
Made by Milton Bradley, 1987.
(plastic, 5 inches)
Remove the hexagonal pieces from the pegs and then try to put them back so that the numbers on all edges match. Same puzzle as the Circus Seven puzzle,, (numbers 1 through 6 correspond to the colors red, green, blue, yellow, white, and orange). For a computer, the solution space is small: 7 choices for the center piece, 6 choices for the first outside piece, 5 choices for the second, etc., for at most 7! = 5,040 positions to try. Here are the directions that came with it:
Further reading:
Jaap's Page, from: http://www.jaapsch.net/puzzles/circus.htm
a.k.a. Mind Exerciser
Masudaya, Japan, circa 1980's?
(4.25" by 1.75" high plastic box and seven hexagonal plastic pieces)
Arrange the seven hexagons so that adjacent edges match. Like the Circus Puzzler, but a larger size puzzle with different color patterns. This is the same puzzle as Drive Ya Nuts, (the colors red, green, blue, yellow, white, and orange correspond to the numbers 1 through 6).
Further reading:
Jaap's Page, from: http://www.jaapsch.net/puzzles/circus.htm
a.k.a. Color Matcher
Circa 1980's?
(2.9" by 1.5" high plastic box and seven hexagonal plastic pieces)
Arrange the seven hexagons so that adjacent edges match. Like the Circus Seven puzzle, but a smaller size puzzle with different color patterns. Jaap's Page shows a number of other color variations for which this puzzle was made.
Further reading:
Jaap's Page, from: http://www.jaapsch.net/puzzles/circus.htm
a.k.a. Spot Color
Made in China, purchased 2007.
(wood box and six wood circles with colored spots, 4 by 4 by 7/8 inches)
Arrange the six circles in a hexagon arrangement so that colored dots match; here is a closer view of the solution:
Further reading:
Jaap's Page, from: http://www.jaapsch.net/puzzles/circus.htm
Peter Pan Playthings, 1986.
(9.4 by 6.4 by 1 inch cardboard box, plastic base, and 6 plastic hexagons)
Jaap's Page gives two solutions, the one shown above and this one::
Further reading:
Jaap's Page, from: http://www.jaapsch.net/puzzles/circus.htm
Unknown manufacturer.
(7 cardboard hexagons, 2.25" point to point, in a 2.75" x 4" x 3/4" plastic box)
Purchased from Mefferts, 2007.
(plastic bag and 9 cardboard triangles, each 4 inches on a side)
This puzzle comes in a number of patterns, this is the "Dizzy Dolphins" version:
Lagoon Games, 2000.
(2 by 6 inch cardboard box with 37 hexagonal cardboard pieces)
Instructions on the box:Solution provided by the manufacturer (http://www.give-me-a-clue.com):
Lagoon Games 2007.
(plastic box and 18 half hexagon plastic plates, 3 by 5 by 3/4 inches)
Form a big hexagon from the 18 half hexagon pieces so that edges match. Puzzles of some type using half hexagons have been around for a long time (e.g., the 1924 patent of A. Chrehore). Here is the solution provided by the manufacturer (http://www.give-me-a-clue.com):
Further reading:
Crehore Patent, from: www.uspto.gov - patent no. 1,495,576
a.k.a. Other Name
Patented by xxx, purchased from xxx.
(cardboard box and 8 cardboard pieces, 5.2 by 5.2 by 7/8 inches)
Copyright Binary Arts 1993.
(cardboard box and 15 cardboard pieces, 5.2 by 5.2 by 7/8 inches)
Copyright Great American Puzzle Factory, 1996.
(cardboard box and 17 cardboard pieces, 5.5 by 5.5 by 1 inch)
Patented by C. R. Weinreb 2000, made by Albatross Games / Toysmith Group 2006.
Transposer 6.
(6 cardboard pieces, each 3.5" on a side;
front and backs shown above)
Transposer Bonbons.
(6 cardboard pieces, each 3.5" on a side;
front and backs shown above)
Each circle on the plate is either colored or empty, and the problem is to stack the plates so that the two sides are a specified solid colors (Bonbons also gives some easier problems for one side). Jaap's Page presents solutions for these and some similar ones. Here are the problems given in the directions, which list them in order of increasing difficulty:
Further Reading
Jaap's Page, from: http://www.jaapsch.net/puzzles/trixxy.htm
Weinreb U.S. Patent Application, from: www.uspto.gov - no. 2005/0225032
Same manufacture as Transposer 6 and Bonbons.
(4 cardboard pieces, each 3.5", backs shown below fronts in photos above)
Four plates must be stacked so that a path of a specified color on each side color connects the corner dots (and there are easier problems for only one side). Here are the ten problems that the directions list in increasing difficulty:
Tantrix Games 1997.
(holder and 10 plastic hexagonal pieces, 1.6 by 2.25 by 2.25 inches high)
Ten hexagonal tiles (numbered 1 through 10 on the backs) can be arranged in patterns, the highest level challenge being to make a loop of a given color (and matching edges of all adjacent tiles). The two sets shown above have different holders and background color, but the same tile patterns. Below, on the right are excerpts from the directions that came with the puzzles and on the left three ten tile loop solutions that are presented on Jaap's Page together with solutions to related puzzles (yellow and blue are switched from the sets shown here).
Further reading:
Jaap's Page, from: http://www.jaapsch.net/puzzles/tantrix.htm
Tantrix Home Page, from: http://www.tantrix.com
Tantrix Games 1991.
(mesh bag and 10 plastic hexagonal pieces, 1.8 inches point to point)
Like Tantrix Discovery, ten hexagonal tiles (numbered 1 through 10 on the backs) can be arranged in patterns, the highest level challenge being to make a loop of a given color (and matching edges of all adjacent tiles) or to make a pyramid with a continuous line through it. Four colors are used (as compared to three with Tantrix Discovery). Here are solutions presented on Jaap's Page for blue and red loops, a blue pyramid, and three red pyramids (the color white here is yellow there):
Further reading:
Jaap's Page, from: http://www.jaapsch.net/puzzles/tantrix.htm
Tantrix Home Page, from: http://www.tantrix.com
Patented by K. Minami and T. Nishimiya 1984, made by Tomy.
(plastic with colored metal ball bearings, 4.3 inches square by 1/2 inch thick)
Turning a wheel on the side causes the center ring to turn one direction and all the other rings to turn in the opposite direction. When solved, the center ring and three of the outer rings have silver ball bearings, and the other three outer rings have bearings colored red, green, and blue, and the center ring is missing one ball bearing. The one missing bearing allows bearings to be moved around by turning the rings and transferring a bearing from one ring to an adjacent one that currently has the empty position. After mixing it up, it is difficult to get it back to the solved position because rings cannot be rotated individually.
Further reading:
Jaap's Page, from: http://www.jaapsch.net/puzzles/gears.htm
Minami and Nishimiya Patent, from: www.uspto.gov - patent no. 4,468,033
Copyright Eng's I.Q. Company Ltd. 1987.
(metal, 15 inches)
Each of 12 discs is colored with the same eight colors, but in different orders. The two discs on the left and right sides are attached to an arm (that rotates). In the center is a long arm, on its ends two shorter arms, and on their ends arms with pairs of discs. The discs themselves can all rotate. The task is to rotate the arms to place the discs in a straight line and then rotate the discs in such a way that colors match between adjacent discs and also between the left and right ends. The analysis on Jaap's Page shows that there are 12 ways to do this, but only one of them uses all eight colors:
Here is a side view of the arms when the discs are lined up in a straight line (as with a solved position):
Further reading:
Jaap's Page, from: http://www.jaapsch.net/puzzles/spectra.htm
Lamphere's Article, from: http://portal.acm.org/portal.cfm
a.k.a. Katzenjammer, (Great) Tantalizer, Face-4, Cube-4,
Bognar Balls, Taktikolor, Frantic, Diabolical, Damblocks,
Symington's Puzzle
Patented by F. Schossow 1900, this popular version by Parker Brothers 1967.
(standard: four plastic cubes, each 1.25 inches square;
mini: four plastic cubes, each 5/8 inches square)
Arrange the cubes in a line so that each side has four different colors (it is not possible to arrange them so that all colors on a side are the same). The puzzle, in both the standard and the mini version, was sold without a box, wrapped with the directions:
The solution is unique up to the ordering of cubes or rotating them all 180 degrees in one dimension (the mini is the same except that green and red are reversed);
Further Reading
Stegmann's Page, from: http://home.comcast.net/~stegmann/pattern.htm#insanity
Schossow Patent, from: www.uspto.gov - patent no. 646,463
Silkman Patent, from: www.uspto.gov - patent no. 2,024,541
Bognar UK Patent Application, GB 2,076,663.
Efficient algorithms are not known for finding Hamilton cycles (let alone two disjoint ones). However, this is a small graph, and it provides an organized way to search for these two cycles rather than playing with the cubes and trying to remember what has been tried.
- Draw four vertices), and label them green, white, blue, red; it doesn't matter how they are arranged (after solving, the figure below was re-drawn to look nicer).
- Number the cubes from 1 to 4 and for each of the three pairs of opposite faces on each cube, draw an edge between the two vertices of the corresponding colors and label that edge by that cube number (a total of 12 edges).
- Look for a Hamilton cycle (that passes through each vertex once) with a different label on each edge; this cycle is shown with the thick edges below (it is also ok to use set of smaller disjoint cycles but that doesn't help here).
- Find a second Hamilton cycle (or set of cycles) with a different label on each edge, that does not uses any of the edges in the first cycle; this cycle is shown with the hashed edges in the figure below.
- Traverse the thick edge cycle to set the top edges (green to blue set the top and bottom of cube 3, blue to white to set the top and bottom of cube 2, white to red to set the top and bottom of cube 4, and red to green to set the top and bottom of cube 1).
- Set the front/back edges with the hashed cycle by rotating each cube (without changing the top and bottom).
cycle 1: G - 3 - B - 2 - W - 4 - R - 1 - G
cycle 2: G - 2 - B - 1 - W - 3 - R - 4 - G
Parker Brothers, Copyright 1986, made in China.
(same size 1.25 inch plastic cubes as the 1967 puzzle)
Katzenjammer Puzzle, patented by Frederick A. Schossow 1900.
(cardboard tray & sleeve, and four 3/4 inch wood cubes)
Same as instant insanity with red -> hearts, green -> clubs, blue -> diamonds,
white -> spades, and cube 3 has the two hidden faces reversed:
These two puzzles have identical cubes (except the green color of the clubs on the right is faded). Here are the top, front, and back, of the two boxes, which are similar but not the same, and also the bottoms, where the one on the left is blank and the one on the right has promotional text:
FOURACE Puzzle, Britain, 1913.
(cardboard box 1+7/8" x 1+7/8" x 3+7/8", and four paper covered wood cubes,
where the cube edges vary in length from 13/16" to 15/16")
Box says "Provisionally Protected"; Stegman's Page credits J. Slocum as dating this puzzle to Gamage's in Britain 1913. The solution is the same as for the Katzenjammer Puzzle:
Here are the top, front, back, and bottom sides of the box (the box back advertises "The Great Card Puzzle"):
Great Tantalizer Puzzle, provisional patent no. 18945, not dated.
(cardboard box, and four 3/4 inch wood cubes)
Same as instant insanity with green -> white, white -> brown, and cube 3 has the two hidden faces reversed:
Here are views of the left end, top, front, bottom, back, and right end:
Tantalizer, made in England, not dated.
(cardboard box, solution sheet, and four 3/4 inch wood cubes; packaged with tie wraps to cardboard back shown on right above)
Same as instant insanity with yellow instead of white:
The solution sheet that came with the puzzle shows the same solution as above,
with cubes in the order 1, 4, 2, 3 and all rotated 180 degrees:
Here are the directions on the bottom of the box:
Symington's Puzzle, W. Symington & Co., Harborough, England, not dated.
(cardboard tray & sleeve, and four 1 inch cardboard cubes)
Same as instant insanity with red -> IDEAL TABLE CREAM (red), green->SOUPS (light blue), blue -> CUSTARD POWDER (white), white -> GRAVY (red with brown triangle), and cube 3 has the two hidden faces reversed:
Here are views of the top, front, and back (the bottom is the same as the top):
"Face 4" made by Ideal Toy Co. 1980.
(tray, cover, and four 1" pieces,
same as Instant Insanity with red -> green and green -> orange)
"Cube-4", except for name on cover is identical to Face-4.
(tray, cover, and four 1" pieces,
same as Instant Insanity with red -> green and green -> orange)
Hungarian "Bognar Buvos Golyok", patented by Jozef Bogner 1981 (GB2076663).
(4 inches long, 1" diameter, balls rotate in place, white / brown / black balls,
same as Instant Insanity with the 1234 order changed to 3142
and with red -> yellow, green -> red/orange, blue -> green, white -> blue)
Taktikolor, manufactured in Hungary, circa 1980?
(box and four 1.5 inch square plastic pieces with colored paper stickers,
same as instant insanity with green->red, white->yellow, red->green,
and for both cubes 3 and 4 the hidden faces are reversed)
Frantic, Wellingtons Ltd Stamford, UK, 1982.
(box and four 1.5 inch square plastic pieces,
same as instant insanity with green->red, white->yellow, red->blue, blue->green
and with hidden faces of cubes 3 and 4 reversed)
Diabolical, Wellingtons Ltd, Stamford, UK, 1982.
(package and four 1.5 inch square plastic pieces,
same as instant insanity with green->1, white->2, red->3, blue->4,
and with hidden faces of cubes 3 and 4 reversed)
Cat Puzzle, Copyright 1996 K. Miller / Images & Editions Stamford Lincs, England.
(cardboard box 4.25" x 4.25" x 1.5", solution sheet, and four 1.375" plastic cubes)
The box back and solution sheet are shown below. The solution is the same as instant insanity with the hidden faces of cubes 3 and 4 reversed, where red = "WIDE EYED CAT", green = "TABLE CAT", white = "TARTAN CAT", blue = "WHITE CAT" (the columns of the solution sheet correspond to cubes 1, 3, 4, 2):
Crazy Cubes, circa 1960's?
(four 1.25 inch square wood pieces labeled with whisky and numbers;
same as instant insanity with green -> 1, white -> 2, red -> 3, blue -> 4)
Sold solved with plastic over the pieces in a tray, with the directions on the back of the tray and the solution sheet under the pieces, where the cubes are arranged as shown in these photos (left is top and front, right is bottom and back):
By exchanging the right two cubes and then spinning each cube 180 degrees, the same presentation as for instant insanity on the first page is obtained:
Damblocks, Schaper Manufacturing Co., Minneapolis, Minn., 1968.
(package and four 1.2 inch square plastic pieces with colored paper stickers,
same as instant insanity with white->yellow)
Made by RainTree and purchased 2000.
(box and 4 pieces, each 7/8" inches square,
same as Instant Insanity with red -> green, green -> yellow, white -> red)
Made by Mr. Puzzle Australia and purchased 2005.
(tray and 4 pieces, each 1.5 inches square,
same as Instant Insanity with red -> circle, green -> Square, blue -> hexagon, white -> diamond)
Circa late 1800's?
(7/8 by 7/8 by 2.1 inch box with three identical 5/8" wood cubes;
original label on top was lost and replaced by a copy from an identical puzzle)
The Grand Army Of the Republic was a veterans organization formed after the American civil war (see the Wikipedia page). This puzzle has three identical cubes, each colored red, white, and blue on three pairs of adjacent faces. Like the four cube Instant Insanity puzzle, the object is to arrange the three cubes in a line so that each side has no duplicate colors. Below is a solution and its graph (constructed as for Instant Insanity); it is unique up to repositioning the puzzle and reordering the cubes (e.g., replacing cycle 2 by R - 3 - W - 1 - B - 2 - R is the same as rotating 180 degrees, rotating forward 90 degrees, and exchanging cubes 1 and 2):
cycle 1: R - 1 - W - 2 - B - 3 - R
cycle 2: R - 2 - W - 3 - B - 1 - R
Further Reading
Wikipedia Page, from: http://en.wikipedia.org/wiki/Grand_Army_of_the_Republic
a.k.a. The Allied Flags Puzzle
Valentine & Sons, Ltd., Dundee, British Manufacture, circa 1918.
(1 x 1 x 4.4 inch cardboard box and five paper covered 13/16" wood cubes;
labels from Henry's of Manchester are on side and bottom of box;
similar in name and theme to the Allies Flags Puzzle)
The cube sides have flags from World War I (British, French, Belgian, Japanese, Russian). Like the four block Instant Insanity puzzle, the object is to arrange the five cubes in a line so that each side has no duplicate flags. Here are the directions that came with it:
Here are two solutions and their corresponding graphs (constructed in the same way as for Instant Insanity), where in the first both cycles use the same Hamilton path, but in the second the first cycle follows a different route:
cycle 1: BR - 2 - BE - 5 - F - 1 - J - 3 - R - 4 - BR
cycle 2: BR - 3 - BE - 4 - F - 2 - J - 5 - R - 1 - BR
cycle 1: BR - 1 - BE - 2 - R - 3 - J - 4 - F - 5 - BR
cycle 2: BR - 3 - BE - 4 - F - 2 - J - 5 - R - 1 - BR
Circa 1920's?
(left / right bottom: 2.15" x 2.7" x 1" box and 5 paper covered 3/4" wood cubes;
right top: 1.3" x 4.2" x 1" box and and same cubes as puzzle on left)
Similar in name and theme to the Allies Flag Puzzle, cubes have flags from World War I (U.S., British, Red Cross, Russian, Republic Of China). Like the Instant Insanity puzzle, the object is to arrange the five cubes in a line so that each side has no duplicate flags. Here is a solution and its corresponding graph (constructed in the same way as for Instant Insanity):
cycle 1: US - 1 - Russian - 4 - British - 3 - Red Cross - 2 - Republic Of China - 5 - US
cycle 2: US - 2 - Russian - 3 - British - 4 - Red Cross - 4 - Republic Of China - 1 - US
Made in the Czech Republic 1983.
(box and six 1.2 inch plastic cubes)
Each of the six cubes has a different one of the colors red, blue, green, yellow, white, and black on each side. This puzzle is similar to Drives You Crazy, but with a different color pattern. Like the four block Instant Insanity puzzle, the object is to arrange the cubes in a line so that each side has no duplicate colors. Here is a solution and its corresponding graph (constructed the same way as for Instant Insanity):
cycle 1: Y - 1 - B - 2 - G - 3 - W - 4 - BK - 5 - R - 6 - Y
cycle 2: Y - 4 - G - 5 - B - 6 - W - 1 - R - 3 - BK - 2 - Y
Purchased from Mefferts 2007.
(six 1.5 inch foam cubes)
Each of the six cubes has a different one of the colors red, blue, light blue, green, yellow, and orange on each side. This puzzle is similar to Iribako, but with a different color pattern. Like the four block Instant Insanity puzzle, the object is to arrange the cubes in a line so that each side has no duplicate colors. Here is a solution and its corresponding graph (constructed the same way as for Instant Insanity):
cycle 1: Y - 2 - G - 1 - O - 4 - LB - 6 - R - 3 - B - 5 - Y
cycle 2: Y - 3 - O - 6 - G - 5 - LB - 1 - B - 2 - R - 4 - Y
Based on a puzzle produced in 1899; this version made by J. A. Storer, 2011.
(plastic box 1.5" x 2.5" x 3.3", instruction card,
and four 1+3/16" painted wood blocks with vinyl stickers)
Arrange the cubes in a 2x2 array so that all four letters appear on the top and bottom faces, all four letters appear on the left and right sides, and all four letters appear on the front and back sides. The letters are based on the names of two Boer generals, Joubert and Cronje, and two British generals, Buller and Warren, from an 1899 production of this puzzle.
We begin with a different puzzle; here the graph constructed as for Instant Insanity; we use letters to label faces and number the cubes 1 = green, 2 = red, 3 = brown, and 4 = yellow:
The two cycles, labeled by the thick edges and the hashed edges, give the following instant insanity like solution to arranging the cubes in a 1x4 array so that all for sides show the 4 letters; note that unlike the solution for instant insanity, one of the Hamilton cycles is actually a set of two cycles, a self loop and a cycle of three vertices:
cycle set 1: (J - 1 - W - 2 - C - 3 - B - 4 - J)
cycle set 2: (J - 2 - J) (C - 1 - B - 3 - W - 4 - C)
Solution idea: Unlike instant insanity, the graph of the preceding page does not give us a complete solution, because we cannot use disjoint cycle sets to simultaneously set both the top / bottom faces and the sides. Instead, we use each cycle set for a way to set the top / bottom faces that may lead to one or more complete solutions, by searching a new graph that describes the ways that cubes can be in a 2x2 array without changing the top / bottom faces. These secondary graphs are constructed below by going around the sides of each cube in a clockwise direction, where when we go from face X to face Y, we place a directed edge (an edge with an arrow) from vertex X to vertex Y (a total of 16 edges). We now look for cycle sets, but with the rule that the direction of arrows must reverse when going from one cube to an adjacent cube, or stay the same when skipping a corner (that uses a self-loop) and going to the opposite corner.
Solutions based on cycle set 1: Cubes 1 (green) and 4 (yellow) form self-loops; if they are adjacent then the red and green edges can be used to cycle between cubes 2 and 3, and if they are diagonally opposite, then the red and blue edges can be used to cycle between cubes 2 and 3. In both cases, and alternate solution can be formed by exchanging cubes 1 and 4:
Solutions based on cycle set 2: We find a solution based on self-loops for cubes 1 and 4 when they are diagonally opposite (and an alternate solution exchanges cubes 1 and 4):
Further Reading
Boer Wars Wikipedia Page, from: http://en.wikipedia.org/wiki/Boer_war
Patented by Jozef Bogner 1981.
(white / brown bodies, 1.7 inches)
Bolygok means planets in Hungarian. A generalization of the Hungarian version of Instant Insanity ("Bognar Buvos Golyok"). Rotate the balls to make patterns such as each side with all four colors or each side with the same color. The directions that come with it are in a long strip; here are pieces of it:
Further reading:
Jaap's Page, from: http://www.jaapsch.net/puzzles/bolygok.htm
Bognar UK Patent Application, GB 2,076,663.
KMS Industries, Alexandria, VA, 1968.
(plastic, 1.75 inches;
directions are in the bottom)
Take the eight cubes out of the case and arrange them in a single 2x2x2 cube to make different patterns. The cubes have one of the colors red, blue, green, and white on each face. The card that is in the bottom of the cage challenges give a number of challenges, including making each face showing all four colors:
KMS Industries, Alexandria, VA, 1968.
(plastic, 1.75 inches;
directions are in the bottom)
Each of the eight cubes has three colored rods going through it, one in each of the x, y, and z directions (four of the cubes have a red, blue, and white rod, two of the cubes have two reds and a white, one has two reds and a blue, and one has two whites and a blue). Take the eight cubes out of the case and arrange them in a single 2x2x2 cube to make continuous rods of the same color passing through it:
Handle says "Clementoni"; unknown date of manufacture.
(plastic with paper surfaces, 12 pieces, 6 by 6.5 by 1.75 inches)
Position the blocks to make a Disney scene. Newer puzzles of this type are shown on the 2008 Clementoni web page (www.clementoni.com) as their 12 piece "super color cubes".
a.k.a. Spots Puzzle
St. Pierre & Patterson Mfg. Co. 1957.
(cardboard tray and nine 2 x 5/8 inch wood bars with recessed white dots;
shown as the "Spots Puzzle" on pages 98-99, 130-131 of the 1893 Hoffmann book)
Assemble nine 1x1x3 unit bars into a die; from left to right in the photo above, the dots are:Here are close-up views of portions of the back of the box:
1. no dots
2. left end
3. top center
4. top center
5. top left, end right6. top left & right
7. top left & right, end left & right
8. top left & right, end left & right, front right
9. top left & right, end left, front left & right
Pentangle Puzzles And Games, England, 2009.
(plastic box and 9 L-shaped wood pieces, 1+7/8 inches)
Assemble the nine L-shaped pieces into a die, with either legal green spots on the outside or legal red spots. Sold in the green solution, which is a "right-handed" die; the red solution is a "left-handed die". Directions tell how to get a "Certificate of Failure". Here are photos of two stages of taking these two solutions apart:
Copyright Warner Brothers 1992.
(wood base and 8 blocks, 4 inches)
Slide the 8 blocks onto the 4 posts to make a 2x2 cube so that each of the 4 sides shows a single character. Below are photos of the other two solved sides and the blocks arranged to show the 8 distinct characters used (each block has some combination of 4 of these): Tweety Bird, Bugs Bunny, Road Runner, Daffy Duck, Marvin the Martian, Sylvester, Wile E. Coyote, Taz (Tasmanian Devil).
Copyright 2003 & Design Patent 2006 by Use Your Head Unlimited.
(plastic, base + top + 10 pairs of 1" diameter balls)
There are 10 pairs of colored balls, one pair for each of the possible pairs of the five colors white, yellow, orange, pink, and blue:
These pairs must be placed to form a pyramid so that no two balls of the same color are touching. The directions say that you should also not allow the same colors to touch as you are building, even for places that are not visible when the puzzle is completed. This is a relatively easy puzzle that is fun for children. It has more than one solution. The puzzle pictured here is the golf version; the same puzzle has also been advertised / sold with other sports themes (soccer, baseball, basketball, tennis, football).
The manufacturer has filed a number of design patents relating to this puzzle and its junior version. P. Roberts and A. Kuwagaki & S. Takenaka have 1970's patents on pyramids using pieces formed from more complicated arrangements of balls.
Further reading:
Thompson Design Patent, from: www.uspto.gov - patent no. D524,381
Roberts Patent, from: www.uspto.gov - patent no. 3,945,645
Kuwagaki Patent, from: www.uspto.gov - patent no. 3,837,652
Copyright 2000 & Design Patents 2005 by Use Your Head Unlimited.
(plastic, base + top + 5 pairs of 1" diameter balls
There are 5 pairs of colored balls, using the colors white, yellow, pink, and blue (all of the 6 possible combinations except pink-blue):
These pairs must be placed to form a pyramid so that no two balls of the same color are touching. The directions say that you should also not allow the same colors to touch as you are building, even for places that are not visible when the puzzle is completed. This is a relatively easy puzzle that is fun for children; it has fewer pieces that the Smarts Puzzle 4 high pyramid made by the same company. It has more than one solution. The puzzle pictured here is the golf version; the same puzzle has also been advertised / sold with other sports themes (soccer, baseball, basketball, tennis, football).
Further reading:
Thompson Design Patents, from: www.uspto.gov - patent nos. D500,533, D500,534, D500,535, D500,816.
Probably made in Hungary in the 1980's.
(plastic, 3.5 inches)
Made by Tantrix, purchased 2007.
(3 inches)
Rotate the hexagonal and square faces so that the edges match. Fairly easy to solve because by starting at one vertex where three faces meet, there are not many possibilities, and then you can start working your way around. The bottom face of the Hungarian version is plain black. The faces of the tantrix version ("The Rock") can also be snapped off and put on in different positions to make different puzzles.
The 1983 patent of Sasso describes a similar idea for a regular solid shape where pairs of opposite faces rotate together.
Further Reading
Sasso Patent, from: www.uspto.gov - patent no. 4,416,453
Patented by REFO Verlag GmbH 2002.
(plastic, 2.6 inches)
Turn the 6 rings so at each of the 12 places they meet the colors match. This is a slightly simpler and more colorful version of the Turn 12 puzzle that as 24 numbers on each ring (each in the range 3 to 9, where matching is by adjacent numbers summing to 12 - see Jaap's Page). Here are the directions that came with the puzzle:
Further reading:
Jaap's Page, from: http://www.jaapsch.net/puzzles/turn12.htm
REFO DE Patent, from: www.epo.org - patent no. DE20112728
Patented by Rubik 1991, copyright Matchbox 1990.
(3.5 inches)
When assembled, the four sides of the pyramid are red, blue, yellow, and white. Moves consists of unsnapping a portion rotating it and snapping it back on.
Further reading:
Jaap's Page, from: http://www.jaapsch.net/puzzles/triamid.htm
McFarren's Page, from: http://www.geocities.com/abcmcfarren/math/r90/trmd0.htm
Rubik HU Patent. from: www.epo.org - patent no. HU207233
Although cubes and various types of burrs are among the most common shapes for assembly puzzles, beautiful craftsmanship, often from wood, has gone into puzzles of many shapes. Some employ coordinate motion (a term used by Stewart Coffin) where pieces must be slide together simultaneously when assembling.
Patented E. Johnson 1940, David Co. circa 1990's?, lower right circa 1960's?.
(top: 3.5"x2.7"x1.4" box, two 3" wood pieces, and directions;
lower right: 2.5"x1.75"x1/2" plastic box and two plastic pieces)
Further Reading
Johnson Patent, from: www.uspto.gov - patent no. 2,216,915
Designed by Wayne Daniel, made and sold by Interlocking Puzzles 2002.
(Jarrah, 3 pieces, each edge 3.5 inches when assembled)
Box says "MADE IN U.S.A. S.K. & CO.", circa 1950?
(cardboard box and 4 wood pieces, 2.5 inches)
Like the classic Two Piece Pyramid where each piece has been cut in half. Here are photos of it being assembled:
Designed by W. Schneider, copyright Binary Arts, 1998.
(4 identical plastic pieces, 3.25 inches on a side when assembled)
Designed by Wayne Daniel, made and sold by Interlocking Puzzles 2002.
(Jarrah and Maple, 4 pieces, each edge 4.75 inches when assembled;
as shown above, comes apart into two 2-piece assemblies)
Designed by Wayne Daniel, made and sold by Interlocking Puzzles, 2003.
(Paduk and Maple, 4 pieces, 3.5 inches)
Two pairs of identical pieces slide together simultaneously. The solved puzzle has a maple diamond on each face where one point meets the point of a diamond on an edge shared with an adjacent face. Here are views of the start of coming apart, and the four pieces:
To solve, as shown on the left below, determine how to assemble two halves that are in the solved state, spread each apart to just coming apart, and with one par in each hand position carefully so that everything can be pushed together. The photo on the right below shows the side not shown in the photo at the top of this page.
Designed by Wayne Daniel, made and sold by Interlocking Puzzles 2002.
(Jatoba and Maple, 5 pieces, each edge 6 inches when assembled;
as shown above, comes apart into a 3-piece and 2-piece assembly)
Designed by Steve Smith, made and sold by Interlocking Puzzles 2004.
(sequential assembly version: Maple, 4 pieces, 3.5 inches,
simultaneous movement version: Jarrah, 4 pieces, 3.5 inches)
These two puzzles have the same size and shape, with six square faces and eight hexagon faces; they were both designed by Steve Smith of Interlocking Puzzles (Interlocking Puzzles also made a third easer puzzle of the same size and shape that was designed by Wayne Daniel). The one on the left above requires sequential assembly of the four pieces in a specific order. The one on the right requires all four pieces to move simultaneously. Here is some of what the designer said about this simultaneous movement and a photo of the puzzle coming apart:"All four pieces must move simultaneously; there are two pairs of mirror image pieces made from Jarrah. There are 4 "solid" faces where the entire face is part of the same piece and four "multi' faces where the face has sections from three different pieces. Two of the multi faces (which are opposite each other) have a triangular shaped section, a diamond shaped section, and a trapezoid shaped section (the other two have two triangular sections and one larger non-convex section); by holding on to these two faces you can push the puzzle apart (all eight faces remain parallel as the puzzle expands)."
a.k.a. Cuboctahedron
Designed by Steve and Leslie Smith, made and sold by Interlocking Puzzles 2004;
box made by J. A. Storer 2004.
(5 pieces: Jatoba, 4.5 inches,
6 pieces: Peroba Rosa, 4.5 inches,
7 pieces: Jarrah, 4.5 inches,
box is 3/8 inch plexiglass with metal hardware, 5 by 5 by 12 inches)
These three puzzles have the same size and shape, with six square faces and eight triangular faces (corresponding to where the corners of the cube have been truncated). The five piece version was designed by Steve Smith and the 6 and 7 piece versions by Steve and Leslie Smith. Here is some of what they say about these three puzzles:Five piece Truncated Cube: "Each piece is a challenge, even after removing the first three, getting the last two apart and together isn't easy. Reassembly? Let's just say this should NOT be the first polyhedra puzzle of ours you work with."
Six piece Truncated Cube: "A small internal space requires multiple moves to get the first piece out."
Seven piece Truncated Cube: "Unique trilateral symmetry makes this puzzle quite difficult. This puzzle can be thought of as two three piece puzzles, with a key piece that holds it all together."
Designed by Stewart Coffin, purchased from Cubic Dissection 2004.
(wood, 6 pieces, 2.5 inches)
Designed, made, and sold by Stewart Coffin in 1970's and early 1980's.
(mahogany, 3 pieces, 4 inches;
one of 6 puzzles purchased during a visit to Coffin's house in the early 1980's)
Described in Stewart Coffin's book The Puzzling World of Polyhedral Dissections; here is some of what he says in the directions that came with the puzzle:"The one symmetrical face of the assembled puzzle happens to resemble a certain corporate logo. The company wanted a simple puzzle incorporating this pattern for some sort of promotional scheme. So the arrangement of six of the blocks was already determined. All that was required to complete the design was the addition of four more blocks in a sort of triangular pyramid and a judicious choice of glue joints to make it into an interesting interlocking puzzle. So the company got what they wanted - except for one thing. It turned out to be anything but simple!"When apart, it is hard to visualize what it is supposed to look like when assembled (although once assembled, you know you have it). Here are photos showing the piece orientations for assembly and the first of the two steps that puts together the two three block pieces:
Vin & Co., purchased from Bits & Pieces 2007.
(wood, 6 pieces, 3.5 inches)
Here are the directions and solution that were sold with the puzzle:
Designed, made, and sold by Stewart Coffin in 1970's and early 1980's.
(left: Mahogany, 6 pieces, 4 inches
right: Cherry, 6 pieces, 4 inches;
the one on the left was purchased at auction in 2001, the cherry one on the right is
one of 6 puzzles purchased during a visit to Coffin's house in the early 1980's;
Coffin called this cherry one a "crude loose-fitting prototype",
but of course it has terrific fit, and although it has some nicks
and pencil marks on the interior edges, overall it is a beautiful puzzle)
Described in Stewart Coffin's book The Puzzling World of Polyhedral Dissections; here is some of what he says in the directions that came with the puzzle:"To disassemble, grasp the opposite pairs of pieces, and gently pull and wiggle until you discover the combination that separates it diagonally into halves. The wiggle the pieces apart until you discover the strange action that separates each half into three pieces."The name is a joke that implies that each of the three axes is formed from some sort of pair configuration; that is, the implication being that the puzzle works something like a burr, where pieces slide in and out parallel to the three axes. In fact, it splits into two halves of 3 pieces each along a diagonal plane. Then, the two halves each come apart by simultaneous motion of all three pieces. Below, the left shows the two halves and the right shows one of the pairs:
Designed, made, and sold by Stewart Coffin in 1970's and early 1980's.
(Cherry and Rosewood, 6 pieces, 4.5 inches;
one of 6 puzzles purchased during a visit to Coffin's house in the early 1980's)
Described in Stewart Coffin's book The Puzzling World of Polyhedral Dissections; here is some of what he says in the directions that came with the puzzle:"The Augmented Four Corners Puzzle consists of six dissimilar interlocking pieces which assemble in one way only, with one sliding axis, to form a geometrical solid with tetrahedral symmetry."Use the three pieces shown below to put together the top (shown with a rubber band) so that the "legs" that hang down have vertical sides that will slide down onto the other three pieces.
Design Science Toys LTD, Tivoli, NY, circa 1990's?
(wood with magnets, 4 inches)
Wood pieces with magnets, each in the shape of a rhombic hexahedron (a slanted cube), can be assembled into shapes, including the same shape as the Augmented Four Corners puzzle. The sheet that comes with the puzzle motivates the use of these pieces from the angles found in carbon molecules.
Designed, made, and sold by Stewart Coffin in 1970's and early 1980's.
(Rosewood and Tulipwood, 6 pieces, 4 inches;
one of 6 puzzles purchased during a visit to Coffin's house in the early 1980's)
Described in Stewart Coffin's book The Puzzling World of Polyhedral Dissections; here is some of what he says in the directions that came with the puzzle:"This puzzle has the most unusual capability of being assembled into three different symmetrical solid shapes, even though its six pieces are all identical in shape."Four assembled shapes are shown in Coffin's book Geometric Puzzle Design; where he discusses the 4-piece Fusion Confusion; version of this puzzle. One shape is the "star" shown above (6 points running vertically); below are two ways to pull it apart into two sets of three pieces. Another is the "hex ring" (a vertical hexagonal cylinder with a ring around the middle) that is show below, and to its right a way to pull it apart. Note that rubber bands have been used in these figures to hold pieces in place while photographed.
Designed by Stewart Coffin, made by interlocking puzzles 2001.
(Paduak and Guatam, 4 pieces, 3.3 inches)
The four pieces of this puzzle are formed by joining two pairs of the six pieces of the Triumph puzzle. Triumph is described in Coffin's book The Puzzling World of Polyhedral Dissections, and this puzzle is described in his book Geometric Puzzle Design, where he says that it has all of the original four solutions of the original Triumph puzzle, but with "only one confusing diagonal axis of assembly". To make the star shape, first join two pairs, and then slide the two halves together:
Designed, made, and sold by Stewart Coffin in 1970's and early 1980's.
(Mahogany, 6 pieces, 4 inches;
one of 6 puzzles purchased during a visit to Coffin's house in the early 1980's;
handwritten on the directions Coffin says "second, nicks and scratches, poor fit";
of course, as you would expect from Coffin, the puzzle looks great and has a good fit)
Described in Stewart Coffin's book The Puzzling World of Polyhedral Dissections; here is some of what he says in the directions that came with the puzzle:"Examine the six individual puzzle pieces and note that there are three identical pieces which we shall arbitrarily refer to as "left-handed" pieces, and three right-handed pieces likewise identical except that one of them has a tapered hole with a pin stuck into it. To assemble the pinwheel solution, first remove the pin and set it aside. Sub-assemble the three left-handed pieces into one sub-assembly, and the three right-handed pieces into another, and mate the two halves. The resulting solution has an axis of symmetry. The other symmetrical solution, known as the Rosebud solution, requires the simultaneous manipulation of all six pieces."
Designed by Stewart Coffin, made by interlocking puzzles 2002.
(Peroba Rosa, 12 pieces, 5 inches)
In Geometric Puzzle Design, Stewart Coffin says: "Twelve sticks of triangular cross-section with pyramidal end blocks assemble with some difficulty to form a symmetrical interlocking burr." Here is the solution that was sold with the puzzle (pieces are numbered in assembly order):
Step 1: Assemble pieces #1, #2, and #3 to form a triangular base.
Step 2: When in place piece #4 will stand vertically with piece #5 parallel to piece #3. Piece #5 is the only piece with an extra augmentation. Assemble with the augmentation directly to the left of piece #2. Hold #4 loosely to allow #5 to slide in under the hook of #2.
Step 3: When in place piece #6 will be parallel to #4. To assemble, piece #6 hooks around #2 from below and slides up through next to #4.
Step 4: When in place piece #7 will be parallel to piece #1. To assemble, first push piece #1 all the way into the puzzle. This allows piece #3 to move to the left giving room for piece #7.
Step 5: Insert piece #7. Slide piece #3 back to the right and #1 forward.
Step 6: When in place piece #8 will be parallel to piece #2. To assemble, place #8 on the right side by hooking around #4 and sliding through #1.
Step 7: Now the puzzle has enough pieces in place to hold together better. When in place piece #9 will stand vertically, parallel to piece #4 and #6. To assemble, drop #4 down and move piece #7 back away from you. Bring #8 towards you until enough opening is made to allow for #9.
Step 8: Insert #9 by hooking around #3. Push #8 back in place to allow #4 to come back up. Make sure #9 is all the way down to allow #7 to slide back towards you. Bring #9 up to its final place. When in place piece #10 is parallel to #5 and #3. To assemble, hook the end of #10 around #8 and slide left under #9.
Step 9: When in place piece #11 is parallel to #8 and #2. To assemble, first drop #4 and #6 down. Slide #8 all the way towards you. Then move #10 to the left just enough.
Step 10: This allows #11 to be inserted underneath #10 with its end hooking around #7. Slide #10 back to the right. Now #8 slides back to allow #4 up. Make sure #11 is all the way towards you to allow #6 to come back up.
Steps 11 & 12: Move #11 to its final place. Then the key piece #12 moves in parallel to #7 to touch the augmented place on #5.
"Crystall Pyramide", made in China, purchased 2009.
(15 wood pieces and base, 5.75 by 5.75 by 3.5 inches high)
Pieces formed from wood rods glued together must be placed on a base (that has some black rods glued to it) to form a pyramid; here is the solution that was sold with the puzzle:
Received as a gift from D. Storer, 2005.
(Cherry, 12.5 inches assembled)
Pull out the white peg that goes through to make the eyes, and the puzzle comes apart in a mor or less linear fashion; about midway through there is a small compartment containing a wood duck:
B. B. Shackman & Co., New York, circa 1940?
(wood, 1.7 by 1.7 by 2.9 inches; end not shown says "MADE IN U.S.A.)
Unknown maker, circa 1930's?
(wood, 3/4 inches square by 3 inches long)
A simpler 3x3 version (3 wavy horizontal cuts and 3 wavy vertical cuts) of the 4x4 puzzle described on page 109 of the 1893 Hoffmann book.
From the grandfather of J. A. Storer; circa 1900?
(wood, 2.4 by 2.75 by 1.9 inches)
A simpler 3x4 version (3 wavy horizontal cuts and 4 wavy vertical cuts) of the 4x4 puzzle described on page 109 of the 1893 Hoffmann book.
Patented K. Walker & designed with H. Nelson, made by Binary Arts, circa 2000.
(four plastic pieces, 4 x 4 x 3/4 inches assembled)
The four pieces do not simply come apart as it appears they might; careful positioning and twisting is required; here is the solution that was sold with the puzzle:
Further Reading
Walker Patent, from: www.uspto.gov - patent no. 5,409,227
Made in Japan, circa 1960's?
(wood, 1+7/8 inches)
Designed by Oskar van Deventer, made by Eric Fuller 2010.
(Pau Ferro and Quilted Maple, 3 inches)
Five pieces, each composed of the shape of a matchbox cover attached to a matchbox tray assemble to a single shape. Here are the pieces:
The two pieces on the top left slide together, then as shown below the pairs of vertical pieces slide together (and the third step slides the two halves together):
Purchased from Puzzles and Brain teasers EBay Store 2007.
(wood dowel and 6 wood pieces with dowels, 2.75 inches)
Six wood pieces with pegs and a key peg (the key peg has a little pin to make friction so it does not fall out of the solved puzzle). Here are solution steps:
Purchased 2006.
(Walnut and Oak, 8 pieces, 5 inches by 3/4 inches thick)
Assemble three pairs and then push together simultaneously:
Purchased from Mr. Puzzle Australia 2006.
(wood, 11/16" cubes, 2.75" x 3.5" x 2" when assembled)
This puzzle is constructed like Kev's Cubes. Here, 31 wood pieces (30 unit sized cubes and one 1x1x2 piece) are connected by an elastic cord, and must be manipulated into the shape shown in the photo above.
Circa 1980's.
(plastic, 4 inches as assembled above)
A sequence of linked plastic pieces that can an be folded into fun shapes. The "solved" position is a 3D diamond shape shown above that fits into the plastic ball in which the puzzle was sold.
Further Reading
Rubik's Snake Booklet, from: http://www.rubiks.com/World/~/media/Files/hint_snake.ashx
McFArren's Page, from: http://www.geocities.com/abcmcfarren/math/snake2d.htm
McFarren's 3D Page, from: http://www.geocities.com/abcmcfarren/math/snake3d.htm
Wikipedia Page, from: http://en.wikipedia.org/wiki/Rubik's_Snake
Sold by Bits and Pieces 2007.
(aluminum, 4 pieces, 2.5 inches)
Four aluminum pieces fit together; here are four basic solution steps:
Step 1: Identify the two pairs:
Step 2: Put the left pair together:
Step 3: Add the third piece:
Step 4: Slip on the fourth piece:
The great thing about the classic Rubik's Cube is that you don't have a bag of pieces when it is unsolved. Keep it on a coffee table, pick it up, play with it, and put it down when get tired. The original 3x3x3 Rubik's cube started an entire class of manipulation puzzles.
Made by SOCUBE, Kuala Lumpur, Malaysia, 2009.
(plastic, 2.1 x 2.1 x 1 inch;
white opposite yellow, red opposite orange, blue opposite green)
Availabe at McDonalds in the U.K. 2002.
(plastic, 3.5 inches)
A very easy (but cute) puzzle.
Further Reading
Jaap's Page, from: http://www.jaapsch.net/puzzles/morph.htm
Designed by Katsuhiko Okamoto 2007, purchased from Gentosha, Japan, 2009.
(plastic, 2.25 by 2.25 by 3/4 inches;
by the same designer as the Rubik 3x3x3 Void Cube)
Seems to impossibly stay together as sets of three are flipped:
Notation: L (left), R (right), F (front), B (back) denote flip that side.
Jaap's Page presents a computer analysis that shows there are only 192 reachable positions, each requiring at most 8 moves to solve. By just playing with this puzzle it usually does not take very long to solve, or to get it to where it can be fixed with the following simple transformation:
F R F R F R
(flip two adjacent edges)
The directions that came with the puzzle also present the following transformations (after doing the last two, rotate or turn the puzzle over to get the views shown):
Further Reading
L F L R B R
(flip two opposite edges)
L F L R F R
(exchange opposite edges)
F L R B
(flip center and
exchange two opposite edges)
Jaap's Page, from: http://www.jaapsch.net/puzzles/floppy.htm
a.k.a. Magic Floppy Cube
Made in Hong Kong, 2009.
(plastic, 2.25 by 2.25 by 3/4 inches)
A version of the Rubik 1x3x3 Floppy Cube where the cube sizes progress from small to large in both horizontal dimensions; it can be solved in exactly the same way. Fun shapes can be formed:
Unlike the Rubik 3x3x3 Mirror Cube which progresses in all three dimensions, here all cubes have the same thickness and not all unsolved positions have a jumbled shape. In fact, because for this puzzle it is very easy to get back to the square shape, it is perhaps even easier to solve than the normal floppy cube. By randomly mixing and restoring to a square the puzzle is typically quickly solved or in a position where two adjacent edges are flipped, which can easily be fixed with the following transformation (F and R denote flips of the front and right sides, 3 means do it three times):
(F R)3
Designed by Katsuhiko Okamoto, made by Gentosha, Japan, 2010.
(plastic, 2.25 by 2.25 by 3/4 inches)
A generalization of the Rubik 1x3x3 Floppy Cube Rubik 1x3x3 Floppy Cube where a 1x1x2 portion can rotate (see also the Rubik 1x3x3 Floppy Mirror Cube); here are a sequence of three moves to make an edge piece sit up:
Jaap's Page presents an analysis, but by just playing it is relative easy to solve, and it is easy to make interesting shapes, like the one on the left below, and then return the puzzle to flat.
Notation: L (left), R (right), F (front), B (back) denote flip that side, L90 to turn the left side 90 degrees clockwise, B90 to turn the back side 90 degrees clockwise.
Once flat, moves for the 1x3x3 Floppy Cube can be used to solve or to be left with one edge flipped as shown on the right above. To fix this, make the edge opposite to this edge sit up, then use the edge pair flipping transformation from the 1x3x3 Floppy Cube (LFL RBR), and then put the opposite edge back down; all 90 rotations are in pairs, so all movement can be clockwise:L90 B90 L90 L F L R B R L90 B90 L90
Further Reading
Jaap's Page, from: http://www.jaapsch.net/puzzles/floppy2.htm
First patented by Rubik 1983, other patents cover different internal mechanisms.
(plastic, 1.5 inches)
A 3-Step Solution
Notation: L (left), R (right), F (front), B (back), U (up), and D (down) for 90 degree clockwise rotations of the faces, - to do counterclockwise instead of clockwise, and 2 to do it twice; corners are denoted with three letters (e.g., FLD = front, left, down corner).
Step 1. Solve the U layer:Pick any side; to be the U layer and solve it (easy when you don't care what happens to the D layer). The next two steps fix the D layer (reposition as needed to make any one of the other four faces the front).Step 2. Put D layer corners in correct locations (but possibly rotated incorrectly):Use the following 7 moves to exchange two corners:Step 3. Rotate the D layer corners correctly:
FLD <-> FRD: F D F- D- R- D- R
Note: A quick way to do FLD <-> BRD is to precede this by R and skip the final R.Turn the puzzle over, rotate it so that an incorrect corner is in the upper front right, and if there is one or more correct upper corners, one of them is in the upper back right. Now make a note of what color should be on top, and repeat these two steps until the puzzle is solved (it will look mixed up until you are done):
- Repeat until the upper front right corner has the correct top color:
R- D- R D
- Rotate the top layer 90 degrees counterclockwise.
The booklet that comes with the Homer Simpson version describes a similar 3-step solution to the one above, using three sequences:
With our notation, these transformations can be expressed as:
Step 2:FRD <-> BLD: F L D L- D- F- D- ("diagonal swapper")Step 3:
FRD -> BLD -> BRD -> FRD: B L D L- B- L D- L- ("shunter")FRD-, BRD-, BLD-: R- D- R D- R- D2 R D2 ("shifter")
The 3-step solutions presented above employ transformations that may have to be used several times. Jaap's Page presents a solution that uses fewer moves by employing a different transformation for each of the possible situations that may occur for Steps 2 and 3 (the transformations of the three step solutions, or equivalents, are a subset of these):
Step 2.FLD <-> FRD: F D F- D- R- D- RStep 3.
FRD <-> BRD: R F D F- D- R- D-
(Jaap's page does FRD <-> BLD: F- R- D- R D F D- )FLD-, BLD+: R- D- R F- D R- D R D2 F2After solving the top layer, rotate the bottom layer (1 move), use one transformation (7 moves) for Step 2, and one transformation for Step 3 (at most 10 moves where a 180 degree rotation counts as 1), for a total of 18 moves to solve the puzzle after the top layer is solved.
FLD+, BLD-: F2 D2 R- D- R D- F R- D R
FLD-, BRD+: R2 D- R D2 R- D2 R D- R2 D
FRD-, BRD-, BLD-: R- D- R D- R- D2 R D2
FRD+, BRD+, BLD+: D2 R- D2 R D R- D R
FRD-, BRD+, BLD-, FLD+: R2 D2 R D2 R2 D
FRD+, BRD-, BLD-, FLD+: R D F R2 D2 F2 D F- D R2
Jaap's page also gives a detailed analysis for solving the top layer in at most 24 moves (giving at most a total of 42 from any starting position). However, once one has played with the puzzle for a while, solving the top layer can become so easy that you don't really have to think about it. In fact, even people who are not "puzzle people" can get so they solve the top layer in less than 10 seconds on the average, and by just repeatedly randomly selecting a color and solving the top layer for that color, can sometimes stumble upon a completely solved puzzle in a an hour or so.
NOTE: A straightforward approach (but not the fastest) for solving the top layer is to first get three cubes correct (very easy) and then to put in the fourth cube, move two of the correct cubes 90 degrees, move the fourth cube 90 degrees to bring it up, and move the two correct cubes 90 degrees to bring them back. If the fourth cube now turns out to be rotated in incorrectly, again rotate the same two correct cubes 90 degrees, rotate the fourth cube in the same direction that you used to bring it up, and then rotate the two correct cubes back. Now rotate the bottom layer so that the fourth cube is again positioned to go up, and try again. After at most two additional tries it will be rotated correctly.
The Darth Maul figure is large (4 inches high) with a smooth mechanism. The others are small (between 2.25 and 2.5 inches high) from Kellogs cereal boxes in the 2002 time frame; each has two related star wars episode II figures, one on each side.
Darth Maul
Darth Vader / Anikin Skywalker
Obiwan Young / Obiwan Older
Lea / Amidala
Dooku / Emperor
Trooper / Jango
R2D2 - C3PO
Mickey Mouse
(Disney, Spain,
circa 1990?, 5",
sold by Mefferts 2006)
Donald Duck
(Disney, Spain,
circa 1990?, 4")
Bugs Bunny
(Warner Brothers,
1999, PUZZLE
HEADZ LTD, 3.5")
Scooby Doo
(Warner Brothers,
1999, PUZZLE
HEADZ LTD, 3.75")
Batman
(Warner Brothers
1999, PUZZLE
HEADZ LTD, 3.75")
Joker
(Warner Brothers
1999, PUZZLE
HEADZ LTD, 4")
Tom
(Warner Brothers,
1999, PUZZLE
HEADZ LTD, 3")
Jerry
(Warner Brothers,
1999, PUZZLE
HEADZ LTD, 3")
Tasmanian Devil
(Warner Brothers,
1999, PUZZLE
HEADZ LTD, 3.25")
Tweety
(Warner Brothers,
1999, PUZZLE
HEADZ LTD, 2.75")
Mars Marvin
(Warner Brothers,
1999, PUZZLE
HEADZ LTD, 3.25")
Hanshin Tigers Baseball
(circa 2000, 3")
Homer Simpson
(circa 2000, 5")
Bart Simpson
(circa 2000, 4.5")
Dog, Kitty, Penguin
(China, 2006, all three are 4.25")
Rubik's Pocket Cube (1980's, 1.5")
Large Size (2006, 2")
Tiny Size (2006, 1")
Keychain (2007, 1")
2007 Calendar Cube (2")
Rubik's Junior (2006, 1.5")
Popeye (1980's, 2.2")
Smaller Popeye (1980's, 2")
Harry Potter (circa 2000, 2.25")
Australian Road SIgns (circa 2000, 2.25")
Jaap's Page, from: http://www.jaapsch.net/puzzles/cube2.htm
Rubiks.com booklet, from: http://www.rubiks.com/World/Rubiks%20downloads.aspx
Rubiks.com assembly diagram, from: http://www.rubiks.com/World/Rubiks%20downloads.aspx
Rubik Patent, from: www.uspto.gov - patent no. 4,378,117
Li Patent, (Eastsheen Mechanism), from: www.uspto.gov - patent no. 5,826,871
Patermann EP Patent (Mickey Mouse), EP712,649.
Khoudry International Patent (K-Ball), IP25874.
Kremmer Patent (Darth Maul), from: www.uspto.gov - patent no. 6,217,023
Nicholas Patent (uses magnets), from: www.uspto.gov - patent no. 3,655,201
Made by J. A. Storer from a standard Rubik 2x2x2 cube, 2007.
(two brass plates glued to a Meffert's Eastsheen Rubik 2x2x2 cube, 2 inches)
This is a relatively easy puzzle that can usually be solved without too much effort by playing a bit. However, it can get more mixed up than is first apparent. An organized way of solving is to combine repositioning of the bandaged portion with transformations for the standard Rubik's 2x2x2 cube that only use R and D rotations, such as these which are shown on Jaap's Page.
Notation: R (right) and D (down) for 90 degree clockwise rotations of the corresponding faces, - to do counterclockwise instead of clockwise, and 2 to do it twice; corners are denoted with three letters (e.g., FLD- = counterclockwise rotation of the front, left, down corner).FLD-, BRD+: R2 D- R D2 R- D2 R D- R2 D
FRD-, BRD-, BLD-: R- D- R D- R- D2 R D2
FRD+, BRD+, BLD+: D2 R- D2 R D R- D R
FRD-, BRD+, BLD-, FLD+: R2 D2 R D2 R2 D
Further Reading
Jaap's Page, from: http://www.jaapsch.net/puzzles/cube2.htm
Made by J. A. Storer from a standard Rubik 2x2x2 cube, 2007.
(four brass plates glued to a Meffert's Eastsheen Rubik 2x2x2 cube, 2 inches)
This is an easy puzzle, but still fun, that can be solved without too much effort by playing a bit.
a.k.a. Rubik 2x2x2 Super Square
Made in China, 2010.
(plastic, 2.2 inches)
Works like a Rubik 2x2x2, and also each face has a circle that rotates. So this puzzle is a bit like a 2x2x2 nested inside a standard 2x2x2 cube.
Two, three, or four Rubik's 2x2x2 cubes joined, purchased from UK3 2005.
(plastic, each formed from 7/8 inch 2x2x2 cubes inches)
a.k.a. Slim Tower, Franken Tower
Made by Gentosha, Japan, 2009.
(plastic, 1.5 x 1.5 x 2.25 inches,
opposite red is yellow, opposite blue is light green, and opposite gray is black)
An extended Rubik's 2x2x2 where two dimensions are restricted to 180 degree rotations.
Notation: With a 2x3 surface facing you, F (front), B (back), U (up), and D (down) denote 180 degree clockwise rotations of the corresponding faces, L (left) and R (right) denote a 90 degree clockwise rotation of the corresponding faces, - to rotate counterclockwise instead of clockwise, 2 or 3 to do it two or three times.
Solution: The solution that comes with the puzzle gives the following transformations that may be used to solve the corners and edges independently.Solve the corners using the following transformation as needed:BRU <-> BRD: U F R F L- U L U R- U RSolve the edges using the following transformation as needed:UF <-> UB: (U R2)3
Further Reading
Jaap's Page, from: http://www.jaapsch.net/puzzles/cube223.htm(Presents a similar approach with many additional transformations.)
Made in Japan, purchased from Mefferts 2010.
(plastic, 1.7" x 1.7" x 3.4"
green opposite yellow, red opposite orange, white opposite blue)
Unlike Rubik 2x2x3, 90 degree turns on the long dimension can lead to jumbled shapes; here is a sequence of three 90 degree turns:
Solution
1. Return the puzzle to the correct shape.One approach is to think of this as a 2x2x2 cube formed by the center portion with stuff hanging off of it, and employ Rubik 2x2x2 transformations.2. Use a solution for Rubik 3x3x4.(Steps to correct edge pieces can be omitted).
Designed by Erno Rubik 1983; left purchased circa 1985; right purchased 2009.
(plastic, 1.5 inches high by 2.25 inches square)
Put the numbers in order on both sides.
Notation: R for a flip of the right side, U, D for clockwise rotations of the up and down faces (- for counterclockwise, and 2 to do it twice). We also use M to denote rotating the whole puzzle 90 degrees clockwise (with respect to looking down), as a convenience so that only right flips are needed (easier to hold and also useful for the solution to Rubik 3x3x4).
Move pieces to their correct layers:
1. Repeatedly position pairs of edges on the wrong layers on the right and do R.
2. Repeatedly position two corners on the wrong layers at the front right and do:Exchange UFR and DFR: R U R U- RSolve the two layers independently:
3. Use this to permute corners; X = Step 2 transformation, Y = reverse of X:Exchange URF and URB: X M- Y D-4. Use this to permute edges:Exchange UF and UR: (R U)2 (R U2)2 XJaap's Page presents the transformations above (and others), as well as the following transformation to change a side to its mirror image (F denotes a front flip):Further reading:
R F T- F T2 R (T F)2 T2 R T- F R
Jaap's Page, from: http://www.jaapsch.net/puzzles/domino.htm
McFarren's Page, from: http://www.geocities.com/abcmcfarren/math/rdml/rubdom1.htm
Made in China, purchased 2010.
(plastic, 1.5 inches high by 2.5 inches diameter)
A smaller version of Rubik3x3x3 Layered and mechanically the same as Rubik2x3x3, but with each layer being a single color (and this version has been made in a circular shape).
Although any solution for Rubik's 2x3x3 could be used, the puzzle is much easier to solve. It is easy to flip the sides as needed to make the centers match the edges (i.e., each side has a cross of a single color). Then corners can be fixed with just 180 degree rotations of the front (F2) and clockwise or counter-clockwise rotations of the top (U, U-). If you want to memorize a simple transformation, this one exchanges the front top left corner with the front bottom left corner:F2 U F2 U- F2After the above transformation has been used to fix pairs of corners, such shown below on the left, a flip of the front and back sides followed by a flip of the left and right sides gives the checkerboard pattern shown below on the right.
Patent filed by Erno Rubik 1975, sold by Ideal Toys in the 1980's.
(plastic with colored stickers, 2.2", keychain 1.2")
A Corners-First Rubik's 3x3x3 Solution
Notation: L (left), R (right), F (front), B (back), U (up), D (down) for 90 degree cockwise rotation of those faces, M for 90 degree clockwise rotation (looking down from the top) of the layer between U and D; - means do counterclockwise instead. Edges on the U layer are UF, UB, UL, UR, on the D layer DF, DB, DL, DR, and on the middle layer MLF, MLB, MRF, MRB. A move or a sequence followed by 2 or 3 means to do it two or three times.
Step 1. Solve the corners using a solution for Rubik's 2x2x2.
Step 2. Position U and D edges by moving to and from the middle layer:Step 3. Use this to flip U and D edges:
- Place the UL, UB, and UR edges by repeatedly positioning the cube so one of them is MRB, rotating the U layer so that the destination is in the UF position, doing F M F-.
Note: These three moves do MRB -> UF, UF -> DF, DF -> MLB, and are a simple way to move a piece from the middle (by first rotating the middle to put the piece in the MRB position) to a position on top (by first rotating the top appropriately). They also have the side effect of moving UF down to DF and recycling DF back to the middle. After each transformation, rotate the U layer back to where it should be.
- Turn the cube over, and repeat Step A.
- Move the edge that goes to DF to the UF position; then move final edge to UF.
Flip the UF edge: F- M (F M)2 F-Step 4. Use rotations of the middle layer and these to position M edges:Front back swap, MLF<->MLB, MRF<->MRB: (R2 M2)2Step 5. Use this to flip M edges (for right to left diagonal, do B2 before and after):
Clockwise cycle, MRF -> MLB -> MRB -> MRF: R2 M R2 M-Flip MRF and MRB: (R M-)3 R M2 R (M- R)3
Notation: L (left), R (right), F (front), B (back), U (up), D (down) for 90 degree cockwise rotation of those faces; - means do counterclockwise instead. Edges on the U layer are UF, UB, UL, UR, edges on the D layer are DF, DB, DL, DR, and edges on the middle layer front are MLF, MRF. A move followed by 2 means to do it twice.
- Solve the bottom layer (easy when you don't care about the rest of the puzzle).
- (Solve the M edges.)
Rotate the M layer so the centers are correct, and then repeatedly position the puzzle so that the UF edge has the correct color facing you and it needs to be moved to MLF or MRF (these 8 move sequences keep edges correctly flipped):UF -> MLF: U- L- U L U F U- F-
UF -> MRF: U R U- R- U- F- U F- (Flip the U edges so they all have the correct color facing up.)
Rotate the U layer so that the UL edge has the correct top color, or if none of the U edges have the correct top color, first do these 6 moves and then two of them will. Then repeat these 6 moves one or two more times to make all of the U edges have the correct top color.F R U R- U- F-- (Move the U edges to their correct positions.)
Repeatedly re-position and use these 8 moves to exchange UF and UL:R U R- U R U2 R- U- (Position the U corners.)
Repeat these 8 moves until at least one U corner is correct (but may be rotated), rotate the cube so the up front right corner is correct, and then continue repeating these 8 moves until all U corners are in their correct positions:U R U- L- U R- U- L- (Rotate the U corners.)
Re-Position the puzzle so that an incorrect corner is in the upper front right, and if there is one or more correct upper corners, one of them is in the upper back right. Now repeat these two steps until all of the upper corners are correct (it will look mixed up until you are done):
- Repeat these 4 moves until the upper front right corner is correct:
R- D- R D
- Rotate the top layer 90 degrees counterclockwise.
25th Anniversary Cube, 2.2"
Gold Cube, 2.2"
all plastic with no stickers, 2.2"
large all plastic with no stickers, 3.5"
Large Dice Cube, 3.5"
Large Alphabet Cube, 3.5"
White Maze Cube, 2.2"
Yellow Maze Cube, 2.2"
Sudoku Cube, 2.2"
Red Sudoku Cube, 2.2"
McDonalds, 2.2"
Chex Cereal, 2.2"
Jack Daniels, 2.2"
UPS, 2.2"
Mickey Mouse, 2.2"
MatLab, 2.2"
Small Cube, 1.2"
Small Shiny Cube, 1.2"
Dice made by Volker (Germany), 2.2"
Assembly Cube, 2.2"
Here are the pieces of an original Rubik's Cube that consist of a central axis assembly and 20 pieces that interlock with it.
Beust's Page, from: http://beust.com/rubik
Bieber's Page, from: http://www.ronaldbieber.de/Fun/Rubik
Chess And Poker Page, from: http://www.chessandpoker.com/rubiks-cube-solution.html
Cheyer's Page, from: http://www.ai.sri.com/~cheyer/rubiks/rubiks.html
Dedmore's Page, from: http://www.helm.lu/cube/solutions/rubikscube
Dry Erase Board Page, from: http://www.thedryeraseboard.com
Fridrich's Page, from: http://ws2.binghamton.edu/fridrich/cube.html
Jaap's Page, from: http://www.jaapsch.net/puzzles/cube3.htm
Jasmine Page, from: http://peter.stillhq.com/jasmine/rubikscubesolution.html
Jeays' Page, from: http://jeays.net/rubiks.htm
JJuergen's Page, from: http://www.mathematische-basteleien.de
Marshall's Page, from: http://helm.lu/cube/MarshallPhilipp
McFarren's Page, from: http://www.geocities.com/abcmcfarren/math/rc/RubCub0.htm
Monroe's Page, from: http://www.alchemistmatt.com/cube/rubik.html
Nerd Paradise Page, from: http://www.nerdparadise.com/puzzles/333
Olefsky Puzzle Solver Page, from: http://www.puzzlesolver.com
Oxford ComLab Text Solution, from: ftp.comlab.ox.ac.uk
Petrus' Page, from: http://lar5.com/cube
Rob's Rubik Repair Page, from: http://www.roobik.com/cgi-bin/rubix/rubix.cgi
Rubiks.com Solution, from: http://www.rubiks.com
Scared Cat Page, from: http://www.scaredcat.demon.co.uk/rubikscube/the_solution.html
Shon's Rubik's Place Page, from: http://www.rubiksplace.com
Solve Rubik Page, from: http://www.solverubik.com
Still's Page, from: http://peter.stillhq.com/jasmine/rubikscubesolution.html
WikiHow Page, from: http://www.wikihow.com/Solve-a-Rubik's-Cube-(Easy-Move-Notation)
Some Rubik 3x3x3 Patents
Rubik Hungarian Patent, BE887875.
Rubik U.S. Patent, from: www.uspto.gov - patent no. 4,378,116
Sugden Patent, from: www.uspto.gov - patent no. 6,974,130
Sugden Design Patent, from: www.uspto.gov - patent no. D495,378
Scott Patent Application, from: www.uspto.gov - application no. 2010/0230897
Further Reading
God's Number is 20, from: http://www.cube20.org
22 Moves, from: http://www.springerlink.com/content/q088143tn805k124/fulltext.pdf
Speed Solving Page, from: http://www.speedsolving.com/wiki/index.php/Main_Page
Superflip, from: http://www.speedsolving.com/wiki/index.php/Superflip
Rubiks.com Page, from: http://www.rubiks.com
Rubiks.com booklet, from: http://www.rubiks.com
Rubiks.com diagrams, from: http://www.rubiks.com
Cube Lovers Archive, from: http://www.math.rwth-aachen.de/~Martin.Schoenert/Cube-Lovers
Wikipedia Page, from: http://en.wikipedia.org/wiki/Rubik%27s_cube
Wikipedia - God's Algorithm, from: http://en.wikipedia.org/wiki/God%27s_algorithm
Wikipedia - solutions, from: http://en.wikipedia.org/wiki/Optimal_solutions_for_Rubik's_Cube
a.k.a. Yong Jun Cube
Purchased from Yong Jun Toys / Mega House, 2009.
(plastic with silver stickers, 2.25 inches)
A version of the standard Rubik's 3x3x3 cube cube where the cube sizes progress from small to large in all three dimensions. Each piece is distinguished by its shape rather than it color. Here are photos of three successive moves:
Any solution for the standard Rubik's 3x3x3 Cube can be used, although it may be more confusing to identify each piece based on its shape when the puzzle is mixed up than it is to look at colors on a standard cube.
Designed by T. Fisher, purchased from Mefferts 2009.
(plastic, 2.2 inches;
silver opposite gold, green opposite blue, red opposite orange;
also made with a black body)
Works just like a a standard Rubik's 3x3x3 Cube, but can be confusing when the shape becomes very jumbled. Meffert's also made this puzzle in all silver and all gold, and versions from China were sold as the "Square King":
Here are photos of 4 consecutive moves:
a.k.a. Holey Cube
Designed by Katsuhiko Okamoto 2007,
top by Gentousha 2009 and uses stickers,
bottom two purchased from CubeFans 2009 and are all plastic.
(plastic, 2.25 inches;
top: gray opposite black, red opposite yellow, blue opposite light green;
bottom: green opposite blue, yellow opposite white, red opposite orange)
By the designer of the Rubik 1x3x3 Floppy Cube. Logically the same as the classic Rubik's 3x3x3 Cube, but mechanically very different. The standard Rubik's 3x3x3 cube relies on central 3D axes to which the centers are attached and the other pieces flow around. Here, one can look through the center of the cube along any of the three axes (i.e., a square bar with a 1x1 unit cross section can be passed through the cube in any of the three directions).
This puzzle can be more confusing than the standard Rubik 3x3x3 because, although the absence of centers should if anything make the solution simpler, without them one does not have the convenient orientation that the centers usually provide. Also, one can end up with an apparent impossibility (often called the void cube parity problem) where the puzzle is solved except that just two edges or two corners are exchanged (which can't happen with a standard Rubik's 3x3x3 cube). Such a configuration corresponds to a standard Rubik's 3x3xx3 cube where in addition to the two exchanged edges or corners, some middle tiles are messed up as well (not an issue here).
When using a corners-first solution to the standard Rubik's 3x3x3 cube with this puzzle, at the last phase that solves the middle layer, the same sequences can be used, possibly preceded with an additional 90 degree rotation of the middle layer (that is, if just two edges need to be exchanged, a 90 degree rotation makes it so either two pairs have to be exchanged or three need to be cycled, both of which are a case for the last phase).
a.k.a. Cornerless Void Cub
Left: made by Smaz Smart Toy Shop IQ Toys from a Gentosha Void Cube 2009.
right: mass produced by Cube For You (C4Y) 2009;
(plastic, 2.25 inches,
left: white opposite yellow, blue opposite green, orange opposite red,
right: blue opposite green, purple opposite red, and yellow opposite gray;
left looks nice, right has a smoother mechanism)
A simplified Void Cube that removes everything but the edges from a standard Rubik 3x3x3 Cube; complements the Rubik 2x2x2 Cube that removes everything but the corners.
The puzzle has exactly two solutions. To see this, observe that for each color there is exactly one other color for which it shares no edge, so this determines the pairs of colors that are opposite each other. Now choose two adjacent colors to make a standard orientation with one on the top and one on the front (for example, for the puzzle on the left above, blue on top and purple on front), which uniquely determines the bottom and back colors, and now it is possible to solve the puzzle with either choice for the left and right colors.
Although a solution for the void cube can be used here (omitting solving corners), shorter sequences can be employed because there is no need to avoid disturbing the corners when manipulating the edges.
Rubik's 3x3x3 with graphics on the middle squares, produced in 1988.
(plastic, 2.1 inches)
Many promotional versions of the standard Rubik's 3x3x3 cube have graphics printed on the faces that require the middle square to be properly oriented. Rubik's 3x3x3 Fourth dimension adds minimal graphics for this purpose. Here are the directions from from the box lid:
Some Rubik's solutions, such as Marshall's Page, employ transformations that preserve center orientations. For others the centers can be fixed at the end with simple moving around and rotating of the middles that does not affect the remainder of the puzzle. The Dry Erase Board Page gives the following idea:0. Optional: Rotate an outside layer (or more than one if you want).Jaap's Page gives specific transformations.
1. Rotate a middle layer.
2. Rotate a different middle layer.
3. Reverse step 1.
4. Reverse step 2.
5. Reverse step 0.
Further reading:
Jaap's Page, from: http://www.jaapsch.net/puzzles/cube3.htm
Dry Erase Board Page, from: http://www.thedryeraseboard.com/mechpuz/333/centersolve
Marshall's Page, from: http://helm.lu/cube/MarshallPhilipp/Rubikfourth.htm
Custom made Rubik's 3x3x3, one color per layer, purchased 2006.
(plastic, 2.2 inches)
Mechanically the same as Rubik's 3x3x3, but with each layer being a single color. Although any solution for Rubik's 3x3x3 could be used, the puzzle is much easier to solve; the solution below is the same as that for the Rhombi Diamond.
Solution:
1. Solve the middle layer.Easy if you don't care about the rest of the puzzle.2. Solve the top and bottom edges.Easy by using 180 degree front rotations to exchange incorrect edges.3. Solve the bottom back right and bottom back left corners.It is easy to play with top rotations and 180 degree front rotations to make at least one bottom corner red; rotate this corner to the bottom back right. If the bottom back left corner is green, play some more with these rotations to make the top front left and top front middle red, then rotate the front 180 degrees to bring these two red cubes down, and then rotate the bottom 90 degrees to bring the red corner to the back right (and making the red corner that was in the back right now in the back left).4. Solve the remaining incorrect corners.This can be done with just 180 degree rotations of the front (F2) and clockwise or counter-clockwise rotations of the top (U, U-). If you want to memorize a simple transformation, this one exchanges the front top left corner with the front bottom left corner:F2 U F2 U- F2
Ideal Toy Co., 1981.
(plastic 2.2 inches, with cardboard can with plastic lid)
A standard Rubik's 3x3x3 Cube for which each day of the year one can solve the top face to that day. It is much easier than the standard cube, since only one side has to be solved. For a given day, the top left and bottom right corners of the top face are blank, the top middle square has day, the top left has one of Sun, Mon, Tues, Wednes, Thurs, Fri, Satur, the middle three squares are the month, JAN, FEB, MAR, APR, MAY, JUN, JUL, SEP, NOV, DEC, and the bottom right two squares are the date (or just the bottom right if the date is only one digit).
Here is a Dutch version Here is a Dutch version solved for Monday, Jan 1 on the left, and on the right the other three sides for this solution (in Dutch, day=dag, Sunday through Saturday are Zondag, Maandag, Dinsdag, Woensdag, Donderdag, Vrijdag, Zaterdag, and January through December are Januari, Februari, Maart, April, Mei, Juni, Juli, Augustus, September, Oktober, November, December).
a.k.a. Bicube
Made by Mefferts, 2009.
(plastic, 2.3 inches)
Although the bandages restrict the way in which this cube can be mixed up, the sequences to solve it are also restricted, making this puzzle reasonably difficult. See Jaap's Page for an analysis of solution sequences. It is easy to make one from a standard Rubik's 3x3x3 Cube by dripping a little glue between the cubes to be fused together and using some larger stickers:
Further Reading
Jaap's Page, from: http://www.jaapsch.net/puzzles/bandage.htm
a.k.a. Fused Cube
Purchased 2008.
(plastice, 2.2 inches)
Here is what the other three sides look like:
a.k.a. Brick Cube
Made by Hidetoshi Takeji, 2008.
(plastic, 2.2 inches)
This is a Rubik's 3x3x3 cube that has been patched in pairs along two of the three dimensions; to see this, rotate the middle section by 90 degrees:
Here is what the other three sides look like:
Designed by Katsuhiko Okamoto, purchased in Japan, 2010.
(plastic, 2.2 inches square)
Like a standard Rubik 3x3x3 cube but movement is restricted so that a face may only turn in the direction of the arrows. When solved, all faces have consistent arrows and can rotate only in the indicated direction. When mixed up, some faces may have no arrows (and can rotate in either direction) and some faces may have arrows in both directions (and cannot be rotated in either direction). Here are box back and the other three sides:
Made by Cube 4 You (C4U), 2009.
(plastic, 2.2 by 2.2 by 3 inches; white body has opposite sides white / blue, red / orange, green / yellow, the same as the color scheme as the standard Rubik's 3x3x3; black body has opposite sides black / white, red / yellow, green / blue)
This extension of the standard Rubik 3x3x3 cube allows only 180 degree rotations in two of the dimensions. One solution approach is to think of an "outer" Rubik 2x2x3 Domino formed by the top and bottom layers with an "inner" domino in the middle:
1. Solve the outer domino.
2. Solve the inner domino, except if your solution makes use of flips of the front, back, or left sides, replace each such flip by a flip of the right side (that is, rotate the middle layers appropriately, flip the right side, rotate the middle layers back).
3. If Step 2 ended up using an even number of flips, then the puzzle is solved. Otherwise, perform the following transformation, adapted from Jaap's Page for the domino, that does nothing to the middle two layers (by exchanging an upper and lower middle edge) using an odd number of flips:D2 R M- (D2 R) 3 M R D2Further Reading
Notation: R denotes a flip of the right face, M a 90 degree clockwise rotation of the middle two layers (with respect to looking down from the top), D and D- clockwise and counter clockwise rotations of the lower middle layer (with respect to looking up from the bottom), 2 and 3 mean do it two or three times.
Jaap's Page, from: http://www.jaapsch.net/puzzles/cube334.htm(Presents a similar approach with many additional transformations.)
Made by WitEden, sold by Mefferts 2011.
(plastic, 2.25 inches;
WitEden made a number of variations, many sold by Mefferts,
including smaller heights, white bodies, RoadBlock versions, and Crazy versions)
Here are three successive moves (top, right, middle):
Made by WitEden, sold by Mefferts 2011.
(plastic, 2.25 inches;
a generalization of the standard 3x3x9 version; also sold in a white body)
Here are three successive moves (back two, middle slice, back):
Made by mf8, sold by Mefferts 2012.
(plastic, 2.1" x 2.75" x 3.5", with storage bag 7.4" x 5.75";
white opposite yellow, red opposite orange, green opposite blue)
For all three dimensions, only 180 degree turns are useful.
"Rubik's Revenge";
Patented by P. Sebesteny 1983.
(plastic, 2.5 inches)
Mefferts "Rubik's Master" 2007;
uses the Eastsheen mechanism,
patented by C. Li 1999.
(plastic, 2.3 inches)
Further reading:
Jaap's Page, from: http://www.jaapsch.net/puzzles/cube4.htm
McFarren's Page, from: http://www.geocities.com/abcmcfarren/math/rr/RubRev1.htm
Helm's Page, from: http://www.helm.lu/cube/solutions/revenge
Hardwick's Page, from: http://www.speedcubing.com/chris/4-movelist3.html
Hardwick's Speed Page, from: http://www.speedcubing.com/chris/4speedsolve.html
Jeays Page, from: http://jeays.net/rr.htm
Rubiks.com booklet, from: http://www.rubiks.com/World/Rubiks%20downloads.aspx
Rubiks.com assembly page, from: http://www.rubiks.com/World/Rubiks%20downloads.aspx
Wikipedia Page, from: http://en.wikipedia.org/wiki/Rubik%27s_Revenge
Sebesteny Patent, from: www.uspto.gov - patent no. 4,421,311
Li Patent, from: www.uspto.gov - patent no. 5,992,850
Purchased from Rubik's.com 2006;
patented by U. Krell 1986.
(plastic, 2.75 inches)
Purchased from Mefferts 2007;
uses the Eastsheen mechanism.
(tiled plastic, 2.9 inches)
Mefferts "Mini Professor" 2007;
uses the Eastsheen mechanism.
(plastic, 2.3 inches)
Made by V-Cube 2008;
patent application by P. Verdes 2007.
(plastic, 2.5 inches)
Further reading:
Meffert's Page, from: http://www.mefferts.com/puzzles/profsol.html
Jaap's Page, from: http://www.jaapsch.net/puzzles/cube5.htm
McFarren's Page, from: http://www.geocities.com/abcmcfarren/math/rp/RubPro1.htm
Monroe's Page, from: http://www.geocities.com/alchemistmatt/cube/5by5cube.html
Wikipedia Page, from: http://en.wikipedia.org/wiki/Professor's_Cube
Krell Patent, from: www.uspto.gov - patent no. 4,600,199
Li Patent, from: www.uspto.gov - patent no. 6,129,356
Verdes Patent Application, from: www.uspto.gov - patent application 2007/0057455
a.k.a. V-Cube 6x6x6
Patent application by Panayotis Verdes 2007, made by V-Cube 2008.
(plastic, 2.75 inches;
opposite black is yellow, opposite red is orange, opposite blue is green)
Uses slightly rectangular cubes on the edges and larger square cubes at the corners; works with a click-stop action. The Wikipedia Page outlines a number of solution strategies, and Jaap's Page presents a solution. presents a four phase solution in the same theme as for the larger Rubik 7x7x7 cube. The Verdes patent describes designs as large as 11x11x11. These designs are quite precise and complex. Below are photos of the this puzzle partially disassembled and the pieces that are used; note that some of these pieces are used for filling space that is not seen from the outside.
Further Reading
Jaap's Page,, from: http://www.jaapsch.net/puzzles/cube6.htm
Wikipedia Page,, from: http://en.wikipedia.org/wiki/V-Cube_6
Verdes Solution Page,, from: http://www.v-cubes.com/solutions_1.php
Verdes Patent Application, from: www.uspto.gov - patent application 2007/0057455
a.k.a. V-Cube 7x7x7
Patent application by Panayotis Verdes 2007, made by V-Cube 2008.
(plastic, 3.1 inches;
opposite black is yellow, opposite red is orange, opposite blue is green)
This cube has a slightly bulging shape. The V-Cube 7x7x7 on the left is described in the same patent as the V-Cube 6x6x6 (the patent describes designs as large as 11x11x11), and like that cube, it uses slightly rectangular cubes on the edges and larger square cubes at the corners (the 7x7x7 has continuous action, whereas the 6x6x6 has click stop action).
The Wikipedia Page outlines a number of solution strategies. Jaap's Page presents a solution of four phases:
- Solve the 5x5 areas of each center one at a time.
- "Inner edge pieces" (ones directly adjacent to the center piece on an edge) are matched up to the center edge pieces to form solved triples on each edge.
- "Outer edge pieces" (edge pieces that are one away from the center edge piece) are matched up to the solved edge triplets to form solved quintuplets.
- Any method for solving Rubik's 3x3x3 cube can now be used to finish the solution (the solved 5x5 centers correspond to the Rubik 3x3x3 centers and the solved quintuplets correspond to the Rubik 3x3x3 edges).
Further Reading
Jaap's Page, from: http://www.jaapsch.net/puzzles/cube7.htm
Wikipedia Page, from: http://en.wikipedia.org/wiki/V-Cube_7
Made in China, 2010.
(9x9x9: plastic, 3.75", yellow opposite gray, orange opposite red, blue opposite green
11x11x11: plastic, 4.5", yellow opposite black, orange opposite red, blue opposite green)
The patent for the Rubik 7x7x7 presented designs for up to 11x11x11 cubes. Although it was not produced, there were subsequently a number of other designs for larger cubes, and in 2010 this cube was produced in China.
But even larger Rubik's cubes did not stop here. In February 2011 Oskar Van Deventer presented a Rubik 17x17x17 cube called "Over The Top". It was fabricated using Shapeways 3D printing technology, and made available for purchase on that web page.
Further Reading
Shapeways Page, from:http://www.shapeways.comRubik 17x17x17 Video, from:http://www.youtube.com/watch?v=ihWyzvOM9pkRubik 17x17x17 Disassembly Video, from:http://www.youtube.com/user/OskarPuzzle?blend=2&ob=1#p/u/2/CBY7JRh2YOoChris Hardwick's Page On Big Cube Speed Cubing, from:http://www.speedcubing.com/chris/bigcubes-info.html
Made by Fabio Causarano, 2007.
(plastic, 2 by 3 by 4 inches)
Constructed by combining Rubik's cube mechanisms. In only a few twists the puzzle can become quite jumbled; here is an example of a sequence of four moves:
Referring to the diagram on the right above (which uses the colors gray, orange, and blue to denote the three portions of the puzzle), the center four gray cubes form a solid block to which two essentially separate puzzles are attached; each of the two 2x3 orange sections can be rotated (by temporarily rotating blue out of the way to solve the orange portion independent of the blue, and similarly the blue portion works independent of the orange. The colors are useful to help think about what is going on (although it is not necessarily the case that the colors will be correct whenever the puzzle has the correct shape).
Made by Fabio Causarano, 2007.
(plastic, 1.4 inches)
Like the Evil Cuboid 2x3x4, constructed by combining Rubik's cube mechanisms. Here is an example of a sequence of four moves:
Made by Fabio Causarano, 2007.
(plastic, 2.2 by 2.9 by 3.7 inches)
Like the Evil Cuboids 2x3x4, constructed by combining Rubik's cube mechanisms. Here is an example of a sequence of four moves:
Here is another example of a sequence of 5 moves:
Made in China, 2010.
(plastic, 1.6 inches high by 2.2 inches square,
yellow opposite white, blue opposite green, red opposite orange)
A smaller puzzle in the theme of the Crazy Cube 3x3x3. Each side can be flipped 180 degrees as in a standard Rubik 2x3x3. cube. In the solved state shown above with yellow on top, when grasping the bottom and rotating the top, the yellow face rotates about the center circle. After one flip of an edge, holding the bottom and rotating the top turns the entire top face as with a standard Rubik 2x3x3 cube and rotates the circle in the bottom. Each successive flip of an edge reverses the relative movement of top and bottom. That is, one full side is always connected to the center circle of the other. Here are four successive moves of flip right, rotate top 90 degrees clockwise, flip right, rotate top 90 degrees clockwise:
Crazy Cube Mars, purchased from Mefferts, 2010
(plastic, 2.2 square, white opposite yellow, blue opposite green, orange opposite red;
Crazy Cube 2x3x3 is a smaller puzzle with this theme)
There are two types of faces:Spin Around: The circle in the center stays fixed and the remainder of the face rotates.The Mars member of a series of eight (Mercury, Venus, Earth, Mars, Jupiter, Saturn, Uranus, and Neptune) that differ in the configuration of the faces; it has the following face configuration:
Spin Together: The entire face moves, as in a standard Rubik's Cube.white = around, yellow = togetherHere is a sequence of three clockwise moves of the left, right, and top faces:
blue = together, green = around
orange = together, red = around
a.k.a. WitEden Super Magic Cube
Made by WitEden, sold by Mefferts 2011.
(plastic, 2.25" x 2.25" x 1.75"; also sold in a white body)
In the same theme of Rubik's Cube 3x3x3 generalized to the Crazy Cube 3x3x3, this puzzle generalizes the WitEden 3x3 stacks (that were made as large as 3x3x9) to have the added movement. For this one, the circle turns with the top layer, and the bottom layer turns around the circle; a version was also made where both the top and bottom layers turn around the circle.
Made in China, 2010.
(plastic, 2.6" square, white opposite yellow, blue opposite green, orange opposite red;
Crazy Cube 2x3x3 and Crazy Cube 3x3x3 are smaller versions;
Crazy Cube 4x4x4 Two has a larger center circle)
Faces rotate around the center circle; here is a sequence of three face rotations:
Here is a sequence of 4 rotations about the center:
Jaap's Page presents a solution.
Further Reading
Jaap's Page, from: http://www.jaapsch.net/puzzles/crazy444.htm
Made in China, 2010.
(plastic, 2.6" square, white opposite yellow, blue opposite green, orange opposite red;
Crazy Cube 2x3x3 and Crazy Cube 3x3x3 are smaller versions;
Crazy Cube 4x4x4 Crazy Cube Two 4x4x4 has a smaller center circle)
Faces rotate around the center circle; here is a sequence of three face rotations:
Jaap's Page presents a solution.
Further Reading
Jaap's Page, from: http://www.jaapsch.net/puzzles/crazy444.htm
Designed by Adam G. Cowan, purchased from Mefferts, 2010.
(plastic, 2.2 inches;
yellow opposite white, green opposite blue, orange opposite red)
This puzzle works like a Rubik's 3x3x3 Cube where looking at each face there are three layers that can turn. Here are two views from the top of the two layers turned.
Any move makes a non-square shape, and successive moves make a completely jumbled shape. Here is a sequence of three moves, a clockwise rotation of the back layer, followed by a clockwise rotation of the front layer, followed by a clockwise rotation of the lower right layer:
a.k.a. Pyraminx Cube
Purchased from Meffert's 2007.
(plastic, 2.2 inches)
Here is a photo of the other three sides:
It can be rotated along any of the planes that passes diagonally through the cube:
Jaap's Page credits this puzzle to Tony Durham, says that it was originally called the Pyraminx Cube by Uwe Meffert, that Douglas Hofstadter coined the name Skewb in a 1982 Scientific American article, discusses the relationship of the Skewb to the Pyraminx, and presents a solution. There are a number of variations of this puzzle, including the Skewb Diamond, Super Skewb Diamond, Skewb Ultimate, Skewb Kite, 3D Skewb, and Skewb Ball
Further Reading
Meffert's Page, from: http://www.mefferts.com/puzzles/skewbsol.html
Jaap's Page, from: http://www.jaapsch.net/puzzles/skewb.htm
McFarren's Page, from: http://www.geocities.com/abcmcfarren/math/Skewb.htm
Dry Erase Board Page, from: http://www.thedryeraseboard.com/mechpuz/skewb/solution
A Cubist Page, from: http://www.acubist.com
Augmented Faces Skewb
a.k.a. Polymorphix Limited Edition
Purchased from Meffert's 2008.
(plastic, 2.9 inches)
Same as the Skewb where each face has a protruding piece on it. The colors of each of the four faces of a protrusion must match the color of the corresponding adjacent face, which gives an explicit constraint to the orientation of a face with respect to its corners.
Augmented Corners Skewb
a.k.a. 3D Skewb
Purchased from Meffert's 2008.
(plastic, 2.9 inches)
Same as the Skewb where each corner has been replaced with a protruding piece (that has the same three colors that match the adjacent faces).
a.k.a. Void Skewb
Designed by Tony Fisher, purchased from Mefferts 2010.
(plastic, 2.2 inches)
In the theme of the Rubik 3x3x3 Void Cube, same as the Skewb but without the centers, so that one can look through the center of the cube along any of the three axes (i.e., a square bar can be passed through the cube in any of the three directions).
Designed by Tony Fisher, purchased from Meffert's, 2009.
(plastic with metallic finish, 3.1 inches;
made in a number of colors in addition to gold,
including silver shown above, copper, white, black)
A Skewb mechanism with sections offset; makes a big mess when it is mixed up. In the same spirit as the Rubik 3x3x3 Mirror Block pieces of the cube are distinguished by shape rather than color.
a.k.a. Dinosaur Cube
Described in patent of J. Holloway 2000, first manufactured in the mid 1990's,
left: custom made from a Rainbow Cube mechanism by D. Calvo 2007,
middle two: sold by SMAZ 2011,
right: sold by Mefferts 2011.
(all are plastic, left 2.3 inches, others 2.2 inches,
left three: yellow opposite orange, pink opposite red, blue opposite white
right: yellow opposite white, blue opposite green, red opposite orange)
Each corner can twist. Below are photos of the other three sides and of the puzzle mixed up:
The Dino Cube is one of the most easy (but fun) Rubik's type puzzles. Start by solving a corner and then do adjacent corners, working your way around to the opposite corner. It is not necessary to memorize move sequences. Three-deep reasoning may be needed, like "to rotate this triangle into place, I need to first rotate this corner so it doesn't get messed up (and then rotate it back afterwards), and before doing that I should rotate this other corner".
Further reading:
Jaap's Page, from: http://www.jaapsch.net/puzzles/dinocube.htm
Holloway Patent, from: www.uspto.gov - patent no. 6,056,290
a.k.a. Black Flower Cube, Star Cube, Rex Cube
Made in China, 2010.
(plastic, 2.2 inches;
white body: yellow opposite black, blue opposite green, red opposite orange;
block body: yellow opposite white, blue opposite green, red opposite orange)
Generalized Dino Cube, with two paths across each diagonal; here are 3 successive moves:
Designed by Oskar Van Deventer, sold by Mefferts 2011.
(plastic, 2.4 inches;
yellow opposite orange, blue opposite green, red opposite purple)
In the theme of the Dino Cube, but much more complex; corners rotate in two different layers:
a.k.a. Super Cubix, Cube 21
Patented by K. Hrsel and V. Kopsky 1993, copyright Irwin Toys 1990.
(plastic, 2.1 inches)
Three layers that form a cube when solved. The middle layer has two identical trapezoid pieces that can be in only one of two states, square or nonsquare. The top and bottom each have four 60 degree corner pieces and four 30 degree edge pieces. The only moves are to rotate the top or bottom layers by a multiple of 30 degrees and to make a vertical 180 degree twist along the reference plane that passes through the two middle pieces. The middle can be solved independent of top and bottom. Repeating three times a twist followed by a 180 degree rotation of the top changes the state of the middle (if you don't care about disturbing the top and bottom, a single 30 degree rotation followed by a twist suffices). A twist followed by 180 rotations of the top and bottom, followed by a twist flips the middle upside-down. And we can rotate the top and / or bottom after a sequence of moves to align them with the middle. Hence, we address solving the top and bottom, without worrying about the middle.
The easier problem of getting the puzzle back to a cube shape, but with colors in any arrangement (as in the second figure above) requires no explicit memorization. Gather the 8 edges in the top to form the "flower" pattern; the figure below shows the flower on the left and patterns resulting from 4 twists. The bottom layer below the flower has all 8 corners arranged in a star, however, the four positions resulting from each of the twists all have identical patters on the top and bottom. So the rule for this sequence is "rotate along the major axis of symmetry 4 times" (shown by the dark lines). The only exception is when a twist gives you the same pattern back; in this case, rotate the bottom by 90 degrees before performing the twist (step 3).
Making the flower is not hard. Pairing edges and then combining pairs is the general approach, but you typically cannot avoid having two "stragglers" that are not paired. The key is to get a pair of stragglers separated by exactly two corner pieces; then you can park them in the bottom left, use rotations of the top and twists to get the other 6 edge pieces together, and then twist up the stragglers to become the first and last of the 8. If you get stuck with two stragglers separated by only one corner piece, split a group and rearrange, sooner or later things will work.
We combine approaches of Jaap, Vandenbergh, and Nerd Paradise for a solution of more moves, but requires only 3 non-trivial sequences to be memorized.
Holding the puzzle: Hold in your left hand with Square 1 on the left, your thumb on the short orange section of the front of the middle layer and your finger on the long red section of the back of the middle layer. All twists are relative to the reference plane that goes from the front left to the back right.
Notation: Pieces are denoted by direction U (up), D (down), L (left), R (right), F (front), B (back); UFL corner, BR edge, etc. For moves, / denotes a twist and (x,y) means rotate the top x units and the bottom y units; a positive number is clockwise and a negative number is counterclockwise. For example:change state of middle layer: (6,0) / (6,0) / (6,0) /Step 1: Make the puzzle into a cube, as described on the previous page.
flip the middle layer: / (6,6) /
Step 2: Get all the white corners to the top and all the green corners to the bottom (but not necessarily in their correct locations). If you are at the level that you can make it into a cube, you can easily do this. Get two green together and park them in the lower left. The using rotations of the top and twists get the other two greens together and twist them down.
Step 3: Get all the white edges to the top and all the green edges to the bottom (but not necessarily in their correct locations), using the transformation UB <-> DF:
(0,-1) / (-3,0) / (4,1) / (-4,-1) / (3,0) /
A note on using the puzzle upsidedown: The moves in Steps 4 and 5 are defined for the top layer. To apply them to the bottom layer, turn the puzzle upsidedown, hold the puzzle with Square 1 on the left (your thumb on the long red section on the front and your finger on the short orange section on the back) and precede a move sequence with (-1,1), which restores the reference plane to effectively go from front left to back right.
Step 4: Position corners using the transformation UFL <-> UFR:
/ (3,-3) / (3,0) / (-3,0) / (0,3) / (-3,0) /* Three times to swap diagonally, or do directly using UBL<->UFR:Step 5: Position edges using the transformation UF <-> UR:
/ (3,3) / (3,0) / (3,3) / (3,0) / (3,3) /
/ (-3,0) / (0,3) / (0,-3) / (0,3) / (2,0) / (0,2) / (-2,0) / (4,0) / (0,-2) / (0,2) / (-1,4) / (0,-3) /* Three times to swap opposites, or do directly using UL<->UR:Step 6: Fix the middle layer if necessary.
/ (3,3) / (-1,0) / (2,-4) / (4,-2) / (0,-2) / (-4,2) / (1,-5) / (3,0) / (3,3) /
Other Useful Sequences (that can be used for shortcuts)
Exchange the top and bottom layers:/ (6,6) / (5,-5)Exchange the UF and UB edges with DF and DB (Nerd Paradise "Sequence A"):(1,0) / (-1,-1) / (0,1)Exchange the 4 top edges with the 4 bottom edges:(1,0) / (-1,-1) / (-2,-2) / (-1,-1) / (0,1)Exchange two pairs of corners (from Jaap's page):UFR<->UBL, DFR<->DBR: / (3,0) / (-3,0) / (3,0) / (3,0) / (6,0) /Exchange two pairs of edges (from Jaap's page):
UFR<->UBR, DFL<->DBR: / (0,-3) / (0,3) / (0,-3) / (0,-3) / (0,6) /UF<->UB, DF<->DB: (1,0) / (-1,-1) / (6,0) / (1,1) / (-1,0)Exchange two edge corner pairs (Nerd Paradise "Sequence B"):
UL<->UF, DR<->DF: (1,0) / (-3,0) / (-1,-1) / (3,0) / (1,1) / (-3,0) / (-1,-1) / (4,1) / (-1,0)DL<->DR, DLB<->DRB: / (3,0) / (-3,-3) / (0,3) /
Square 1 is shipped mixed up in a way that looks intimidating but can be solved with 7 twists that are provided in the directions:
Sold in U.K, circa 1990.
(plastic, 2.1 inches)
Sold in Hungary, circa 1990.
(plastic, 2.1 inches)
3 yellow sides with silver on opposite sides.
(plastic, 2.1 inches)
Custom made - all sides gold.
(plastic, 2.1 inches)
All black, purchased from Cubfans 2007.
(plastic, 2.1 inches)
All clear, purchased from Cubfans 2007.
(plastic, 2.1 inches)
Made in China, purchased 2005.
(plastic, 2.1 inches)
"left: Made in China 2010.
Right: "Dodecagonal Barrel", custom made by Laurent Langlade 2007.
(plastic, made with Square 1 parts; 2.2 inches;
top and bottom layer can each rotate by multiples of 30 degrees
and a vertical 180 twist can be made along a single reference plane)
"Super Square 1", by Smaz Smart Toy Shop IQ Toys, Hong Kong, 2008-2009.
(plastic, 2.2 inches high;
extra center layer where everything rotates around a center post that splits;
switching top and bottom layers will not change color of the top of the posts.)
"Two-Layer Square 1, made in China 2011. (plastic, 2.2" x 2.2" x 1.1", a Super Square 1 without the middle layers)
Further Reading
Jaap's Page, from: http://www.jaapsch.net/puzzles/square1.htm
McFarren's Page, from: http://www.geocities.com/abcmcfarren/math/sq1/sq1xf.htm
McFarren's Page2, from: http://www.geocities.com/abcmcfarren/math/sq1/sq1xf.htm
Alchemistmatt Page Page, from: http://www.alchemistmatt.com/cube/square1.html
Dry Erase Board Page, from: http://www.thedryeraseboard.com/mechpuz/square1/solution
Nerd Paradise Page, from: http://nerdparadise.com/puzzles/square1
Vandenbergh's Page, from: http://www.cubezone.be/square1.html
Monroe's Page, from: http://www.alchemistmatt.com/cube/square1.html
Eggermont's Page, from: http://web.inter.nl.net/users/C.Eggermont/Puzzels/SquareOne
Eggermont's List of all Square 1 configurations,from: http://web.inter.nl.net/users/C.Eggermont/Puzzels/SquareOne/SquareList.htmlF2 Page, from: http://f2.org/maths/square1
Hrsel and Kopsky Patent, from: www.uspto.gov - patent no. 5,193,809
Designed by A. Cowan 2005, purchased from Mefferts, 2010.
(plastic, 2+3/8 inches;
black body: red opposite white, yellow opposite orange, blue opposite green
white body: red opposite black, yellow opposite orange, blue opposite green)
Each of the 12 edges can rotate 180 degrees; here is a sequence of three moves:
In addition, an edge may be partially rotated so that subsequent moves create a jumbled shape; here is the same sequence of three moves as shown above except the first is a partial rotation:
Invented by Oskar van Deventer, purchased from Mefferts, 2010.
(plastic, 2.3 inches)
Looks like a complicated version of Rubik's Cube, but is actually much easier to solve (see the Gear Cube Extreme for a harder to solve version). Here is the puzzle solved, the right face rotated 90 degrees, and the right face rotated 180 degrees:
Call the operation of rotating a face 180 degrees a flip; it is the only thing you can do:Jaap's Page presents a solution. Here is an approach that requires essentially no memorization:
- A 90 degree rotation of a face locks up the puzzle.
- Middle layers can only be manipulated by flip operations.
- A flip cycles the adjacent middle layer by 90 degrees and rotates its 4 gear edges by 60 degrees each; 3 flips returns the adjacent middle layer to flat, and 12 flips returns you to exactly where you started. A flip also has the effect of reordering two of the gear edges in each of the other two middle layers.
- Centers move around, but gear edges of a middle layer never leave that layer.
Further Reading
- Restore puzzle to be flat (easy - do flips as needed).
- Solve the corners (easy - faces cannot rotate 90 degrees).
- Use step A to solve as much as possible, use Step B, and repeat until solved (repositioning the cube as appropriate):
- Flip the right face clockwise 6 times.
(Exchanges front/rear and top/bottom of the vertical center layer).
- Flip the bottom face clockwise, flip the right face twice clockwise, flip the bottom face counter clockwise, flip the right face twice counter clockwise.
(Exchanges front/rear of vertical center layer and left/right centers.)
Jaap's Page, from: http://www.jaapsch.net/puzzles/gearcube.htm
Invented by Oskar van Deventer, purchased from Mefferts, 2011.
(plastic, 2.3 inches)
A harder to solve version of the Gear Cube where the edge pieces along the middle layer are not geared; shipped with stickers to go in the black U's below the gears to make a more difficult puzzle that Mefferts calls the "Gear Cube Extreme". Jaap's Page presents a solution.
Further Reading
Mefferts Page, from: http://www.mefferts.com
Jaap's Page, from: http://www.jaapsch.net/puzzles/gearcube2.htm
Designed by Oskar van Deventer and Bram Cohen, made by Mefferts 2011.
(plastic, 2.25 inches)
As shown on the left below, the puzzle spins around (keep spinning and get back to where you started). As shown in the middle below, the difficulty of this puzzle comes from its ability to be split apart along any of the three axes to allow the orientation of two halves to be changed by spinning only one half, as shown on the right below.
Patented by Meffert 1981 and Copyright by Tomy 1981;
metalized version, with click-stop action, purchased from Mefferts 2006.
(plastic with metal surfaces, back is green and bottom is gold, 4 inches;
see also Mefferts Jing's Version of this puzzle)
Notation: There are 4 tips, 4 corners that the tips are attached to, and 6 edges. Holding the puzzle with one of the faces towards you, clockwise and counterclockwise rotations of the top, lower left, and lower right corners are denoted by T+, T-, L+, L-, R+, and R-.
Solution:
1. Orient the tips (and to stay organized, keep them correct after each step).
2. Place the bottom edges (easy when you don't care about the corners).
3. Rotate the top so that at least one of the three remaining edges is correct, and position the puzzle so that this correct edge is in back.
4. The two front edges will now be in position; if they are flipped, do:R- T- L- T+ L+ R+ T+5. Correct two corners at a time with simple 5-sequences that rotate the two front corners, where here x and y are each either + or -, and 5 means repeat five times:(Lx Ry)5Choose + and - to be opposite the direction you want to go.
For example, do L- R+ five times to rotate the front left clockwise (60 degrees)
and the front right counter-clockwise.
Note: If only one corner is incorrect, make it and an adjacent corner incorrect (by rotating in the wrong direction), and then use a second 5-sequence to correct the two. Similarly, three corners can be corrected by correcting one and leaving a second incorrect, and then correcting the remaining two.
If Step 1 is skipped, then after completing Step 2, Step 3 is 1 move, Step 4 is 7 moves, Step 5 is 10 moves to correct two corners or 20 moves to correct 1, 3, or 4 corners, and finally correcting the tips is 3 moves, for a total of 31 moves in addition to Step 2. This is far more than used by an optimal algorithm (Jaap's Page describes a computer analysis that shows that a solution is always possible in at most 11 moves). However, it is a simple method that just boils down to memorizing the sequence of 7 moves for Step 4. Also, if one is careful to choose the easiest face for the bottom and minimize the number of moves for Step 2, the solution compares well with the total of 38 moves mentioned in the directions to the original Tomy version:Other Versions of Pyraminx
Tomy Pyraminx 1981, Mefferts Pyraminx, and Pyraminx Keychain.
(left plastic 4", middle plastic 4", right plastic with chain 1.75")
Further Reading:
Mefferts Page, from: http://www.mefferts.com/puzzles/pyramsol.html
Jaap's Page, from: http://www.jaapsch.net/puzzles/pyraminx.htm
McFarren's Page, from: http://www.geocities.com/abcmcfarren/math/PyrMin.htm
Dry Erase Board Page, from: http://www.thedryeraseboard.com/mechpuz/pyraminx/solution
Nerd Paradise, from: http://www.nerdparadise.com/puzzles/pyraminx
Monroe's Page, from: http://www.alchemistmatt.com/cube/pyramix.html
Meffert Europena Patent, EP042695A2.
a.k.a. Rounded Halpern-Meier Pyramid
Made by Mefferts, 2010.
(plastic, 4 inches;
left: fluorescence labels - back is orange, bottom is green;
right: Cube Smith labels - back is green, bottom is blue)
This puzzle is like the Pyraminx, except it does not have the tips but does have face centers (triangles). We use the same notation for solving, less any reference to tips.
Notation: There are 4 corners and 6 edges. Holding the puzzle with one of the faces towards you, clockwise and counterclockwise rotations of the top, lower left, and lower right corners are denoted by T+, T-, L+, L-, R+, and R-; 3 means do it three times.
Solution:
- Solve the corners and edges with a solution for the Pyraminx.
Note: Without tips to keep you oriented, it can help to determine the colors of the sides once at the start, and then for the remainder of the solving, keep the puzzle in a fixed orientation with the same side facing down and the same side facing you.
- Use the following transformation, given on Jaap's Page, to fix the centers (it exchanges the front and bottom triangles and the left and right triangles):
( R T R- T- ) 3
Further Reading:
Jaap's Page, from: http://www.jaapsch.net/puzzles/PyraminxJing.htm
a.k.a. Crazy Tetrahedron Plus
Purchased from Mefferts, 2011.
(plastic, 3.75 inches)
In the same spirit as the generalization of Rubik's Cube 3x3x3 to the Crazy Cube 3x3x3, this is a generalization of Jing's Pyraminx. Shown above is Meffert's "regular" version that has no restrictions on moves; each face can rotate around the circular portion in its center. Like the Crazy Cube 3x3x3, Meffert's also has produced different move restriction variations, with names of the planets (Mercury, Venus, Earth, Mars, Jupiter, Saturn, Uranus, and Neptune).
Purchased from Mefferts 2007.
(plastic with plastic tiles, 2.5 inches)
This is the same puzzle as the Pyraminx, without the tips (or the same as Jing's Pyraminx without the centers), and the same solution can be used. The colors are arranged so that the yellow triangle is opposite the blue face, the blue triangle is opposite the yellow face, the red face is opposite a green triangle, and the green face is opposite a red triangle)
Note: Without tips to keep you oriented, it can help to determine the colors of the sides once at the start, and then for the remainder of the solving, keep the puzzle in a fixed orientation with the same side facing down and the same side facing you.
Designed by Timur Evbatyrov, made by Mefferts 2011.
(plastic, edges are 3.6", stands 3.4" high;
yellow, orange, blue, green)
A large version of Pyraminx, here are photos of the three types of rotations:
Designed by Timur Evbatyrov, sold by Mefferts 2010.
(plastic, edges are 3" long;
yellow, blue, orabge back, green bottom)
A generalization of the Pyraminx, where in addition to tips and corner sections that rotate, faces can also rotate:
a.k.a. Supernova
Patented by H. Corbeck and C. Bandelow 1982, G. Obermair 1982;
Left Tomy 1982, right Mefferts tiled version 2009.
(plastic, 2.75 inches between opposite faces)
Twelve sides, each a different color, can each be rotated. Jaap's Page gives a solution, mentions the relationship of this puzzle to Alexander's Star and Impossiball (see also Dogic), and has a discussion of a number of origins of this puzzle.
On opposite sides the Tomy version has:red / greenOn opposite sides the Meffert version has:
blue / magenta
yellow / maroon
white (Tomy graphic in center) / orange ("MEGAMINX TOMY" in center)
dark purple / green
light blue / pinklight blue / brownFurther reading:
green / light green
red / orange
white / yellow
purple / pink
blue / dark blue
Meffert's Page, from: http://www.mefferts.com/puzzles/megasol1.html
Jaap's Page, from: http://www.jaapsch.net/puzzles/megaminx.htm
McFarren's Page, from: http://www.geocities.com/abcmcfarren/math/mm/MegMin1.htm
Dry Erase Board Page, from: http://www.thedryeraseboard.com/mechpuz/megaminx/solution
Corbeck and Bandelow GB Patent, from: http://www.ipo.gov.uk - patent no. GB2101491
Obermair DE Patgent, from: www.epo.org - patent no. DE3204033
Wikipedia Page, from: http://en.wikipedia.org/wiki/Megaminx
Mefferts 2009.
(plastic, 2.75 inches between opposite faces)
Like the standard Megaminx but with no center portion; in the same theme as the Void Cube.
On opposite sides the colors are:light blue / orange
green / light green
brown / red
white / yellow
purple / pink
blue / dark blue
a.k.a. Crazy Megaminx
Purchased from Mefferts, 2011.
(plastic, 3.1 inches from face to face)
In the same spirit as the generalization of Rubik's Cube 3x3x3 to the Crazy Cube 3x3x3, this is a generalization of the Megaminx. Shown above is Meffert's "Saturn" version, where for each pair of opposite faces, one rotates around the circle in the center (denoted on the packaging as a "0") and for the opposite side the circle rotates with the face (denoted on the packaging as a "1"); the faces and their colors are:white = 0 opposite gray = 1,Like the Crazy Cube 3x3x3, Meffert's also has produced different move restriction variations, with names of the planets (Mercury, Venus, Earth, Mars, Jupiter, Saturn, Uranus, and Neptune).
red = 1 opposite orange = 0,
green = 1 opposite light green = 0,
blue = 1 opposite light blue = 0,
light yellow = 0 opposite yellow = 1,
pink = 0 opposite purple = 1
a.k.a. Flowerminx
Sold by Mefferts 2009.
(in black and white bodies, plastic, 2.9 inches between opposite faces)
Twelve sides, each a different color, can each be rotated. A simpler version of the Megaminx (see also the Master Kilominx). Here are views of the other six sides:
Both versions use the same colors, except the white face is changed to black when going from the black body to the white body version; on opposite sides the colors are:red / gold
blue / light blue
orange / light purple
yellow / white or black
pink / purple
light green / dark green
Jaap's Page notes that this is the same puzzle as the Impossiball and presents a solution.
Further Reading
Jaap's Page, from: http://www.jaapsch.net/puzzles/impossi.htm
Made by mf8, sold by Mefferts 2012.
(plastic, 3.4 inches between opposite faces, with storage bag 7.4" x 5.75")
Rotations through the center work like the standard Kilominx (where the puzzle stretches a bit); there is an additional layer on all faces that can rotate.
On opposite sides the colors are:white opposite gray
green opposite light green
blue opposite light blue
pink opposite purple
light yellow opposite yellow)
Made by Cube 4 You (C4U), 2009.
(plastic, 3.5" between opposite faces, 4.2" between farthest points)
A larger version of the Megaminx; twelve sides of distinct colors each have two layers that can be rotated.
On opposite sides the colors are:white (with C4U logo in center) / gray
light blue / dark blue
dark yellow / light yellow
light green / dark green
orange / red
purple / pink
Made by Cube 4 You (C4U), 2009.
(plastic, 3.5" between opposite faces, 4.2" between farthest points)
An even larger version of the Megaminx than the Gigaminx: twelve sides of distinct colors each have three layers that can be rotated.
On opposite sides the colors are:white (with C4U logo in center) opposite brown
yellow opposite aqua
blue opposite light blue
purple opposite pink
light green opposite dark green
orange opposite red
Made by Mefferts 2008.
(plastic, in both black and white bodies, 3.5 inches)
Twelve axes of rotation in a similar theme to the Megaminx, but different because here, each of the twelve faces is rotated along a plane that passes through the center of the puzzle. The six faces shown above are orange, green, blue, purple, brown, and white; as shown below, opposite these faces are the colors teal, dark green, dark blue, pink, burgundy, and yellow:
Jaap's Page presents a solution.
Further Reading
Jaap's Page, from: http://www.jaapsch.net/puzzles/pyracrys.htm
Purchsed from Mefert's 2007.
(plastic, 2.5 inches between faces, 4 inches point to point,
opposite faces are light blue / blue, yellow / white, green / light green, red / orange)
Rotation is not about the points of the diamond; rather it is along each of the four planes that cuts the puzzle in half. This puzzle is a variation of the Skewb (it is a smaller version of the Super Skewb Diamond). Jaap's Page presents a solution that is a bit more efficient that applying his solution for the Skewb.
Further Reading
Meffert's Page, from: http://www.mefferts.com/puzzles/solution-skewb-diamond1.html
Jaap's Page, from: http://www.jaapsch.net/puzzles/diamond.htm
a.k.a. Diamond Octahedron
Purchased from the Cuber Shop, Tiawan, 2009.
(plastic, 2.25 inches between faces, 4 inches point to point,
opposite faces white / yellow, orange / black, magenta / blue, green / red)
A larger version of the Skewb Diamond; this is a different puzzle than the Octahedron. Rotation is not about the points of the diamond; rather it is along each of the four sets of two planes that divide the puzzle between opposite faces:
a.k.a. Pyraminx Ball
Purchsed from Mefert's 2008.
(plastic, 3 inches between opposite faces)
There are twelve faces and six colors (red, blue, green, orange, yellow, and pink). When solved, each pair of opposite faces is the same color. Like the Skewb Diamond, rotation is not about the points, rather it is along each of the four planes that cuts the puzzle in half, and this puzzle is a variation of the Skewb. However, Jaap's Page explains that this puzzle is harder because orientation of the components of a face matters, and presents a solution. Mefferts also made this puzzle in a 12 color version (yellow opposite white, light green opposite dark green, pink opposite purple, orange opposite light purple, gold opposite red, light blue opposite dark blue); here are views of the front and back:
Further Reading
Meffert's Page, from: http://www.mefferts.com/puzzles/solution-skewbultimate1.html
Jaap's Page, from: http://www.jaapsch.net/puzzles/ultimate.htm
Designed by Tony Fisher, Purchased from Meffert's 2010.
(plastic, 12 sides, 3" between faces, 4" between farthest points;
uses the Skewb mechanism;
left black body, right white body;
yellow opposite orange,
light green opposite dark green,
light blue opposite dark blue,
gray opposite white,
red opposite pink,
dark purple opposite light purple)
Designed by Tony Fisher, purchased from Mefferts 2010.
(plastic, 2.5" between hex faces, 3" between square faces;
based on the Skewb;
6 square faces are dark green;
8 hex faces are yellow opposite orange, purple opposite pink,
red opposite light green, blue opposite light blue)
Purchased from Mefferts, 2009.
(plastic, 2 inches across minimum dimension;
2.75 inches across farthest points)
Like Rubik's 2x2x2 Rubik's 2x2x2 cube with each corner cut diagonally in half so that the three corner faces become a single face. It is shipped with a solved state of two adjacent yellow faces, two adjacent red faces, two adjacent green faces, and two adjacent blue faces. Mix it up, and then any solution method for Rubik's 2x2x2 can be used.
a.k.a. Figurenmatch, Distortion Demon Square
Patented by Manfred Fritsche 1983.
left: shiny stickers 2007, other sides are red and green, plastic, 3.8";
right: Mefferts keychain purchased 2007, plastic, 2.25" edges)
This puzzle is manipulated by turning along a cutting plane (the tips don't turn). It can be hard to visualize what is going on after the puzzle gets into some strange shapes. It is fairly easy to get it back to the pyramid shape; Meffert's Page, Jaap's Page, and McFarren's Page present solutions where this is the first step, but then the final steps employ transformations that temporarily go through non-pyramid shapes. Using a plain colored version of this puzzle, here are some photos of some of the shapes the puzzle can take.
Further Reading
Mefferts Page, from: http://www.mefferts.com/puzzles/jpmsol.html
Jaap's Page, from: http://www.jaapsch.net/puzzles/pyramorf.htm
McFarren's Page, from: http://www.geocities.com/abcmcfarren/math/pmorph.htm
Wikipedia Page, from: http://en.wikipedia.org/wiki/Pyramorphix
Fritsche DE Patent, from: www.epo.org - patent no. DE3245341
a.k.a. Star of David, Sterns Puzzle
Patented by I. Goldfarb 1985 and B. H. Apsan 1995,
custom made by EBay member jamf55 in Spain 2007.
(plastic, 2.5 inches)
This puzzle is like a Pyramorphix with a pyramid glued to the center of each of its faces, and the same solution sequences can be used; the colors on this one are arranged so that it is solved when the planes induced by the pyramids each are a single color. Here is a photo of the other sides:
Further Reading
Goldfarb Patent, from: www.uspto.gov - patent no. 4,496,155
Apsan Patent, from: www.uspto.gov - patent no. 5,386,993
a.k.a. Master Pyramorphinx
Left two: made by Mefferts 2009;
right two: made by Smaz Smart Toy Shop IQ Toys, Hong Kong, 2009.
(plastic, left 3.8 high", right three 2.75" high;
left three all have the colors yellow, green, red /orange, blue)
A big brother to the Pyramorphinx. Each of the 6 edges of this puzzle can twist. If one stays limited to 180 degree turns of the edges, then this is a puzzle of mixing up the colors and then restoring them, where the puzzle always has its correct shape. However, the fun begins when you employ 90 degree turns to transform the puzzle into a jumbled mess; here are 4 moves using a black body version from Smaz:
This puzzle works like a Rubik's 3x3x3 cube, where each of the 6 edges corresponds to a face of Rubik's 3x3x3, the four vertices of the Mastermorphinx correspond to 4 non-adjacent corners of Rubik's 3x3x3 (e.g., two diagonally opposite corners on top and two diagonally opposite corners in the other direction on the bottom), and the four faces of the Mastermorphix correspond to the other 4 corners of Rubik's 3x3x3 (where a face corresponding to a corner includes a triangular half of each of the three faces incident to that corner). That is, imagine the 6 edges of the Mastermorphix running diagonally across each face of the 6 faces of the cube, where the 6 center pieces of the edges of the Mastermorphix correspond to the 6 centers of the cube, the 4 tips of the Mastermorphix together with the four centers of the Mastermorphix correspond to the eight corners of the cube, and the remaining 12 face sections of the Mastermorphix correspond to the 12 edges of the cube). So any solution for Rubik's 3x3x3 can be used, but in practice this puzzle can be very connfusing when mixed up into a jumbled shape, until one gets used to looking at it. In a theme similar to the Skewb Egg, just getting the shape back with the single color gold version is a challenge.
a.k.a. Cushion Cube
Circa 1980's?
(plastic, 2.2 inches)
A Rubik's 3x3x3 Cube that has been beveled and employs a different color scheme; a solution method for Rubik's 3x3x3 Cube can be used to solve this puzzle.
The solution is not unique since when the top and bottom sections are rotated, the puzzle remains solved. The stickers around the middle are gold, silver, white, and light blue. The top and bottom tips have white stickers. The eight slanted faces have the colors green, orange, blue, light purple, yellow, dark purple, red, and pink, but the arrangement of these stickers may vary from one puzzle to another.
a.k.a. Polish Cushion
Custom made by Mariusz Dabrowski 2007.
(plastic, 2.2 inches wide, 2.75 inches point to point;
yellow opposite green, orange opposite pink)
A Rubik's 3x3x3 Cube that has been beveled and employs a different color scheme; like the Pillow Cube a solution method for Rubik's 3x3x3 Cube can be used to solve this puzzle.
Made by SOCUBE, Kuala Lumpur, Malaysia, 2009.
(plastic, 2.2 inches)
Like the Pillow Cube, this is the same puzzle as a Rubik's 3x3x3 Cube. However, as the name indicates, it is confusing because when orientated as shown in the photo above, the top and bottom layers do not rotate (e.g., referring to the front left corner, the two white triangles and the red triangle are part of a single piece). To see the correspondence with Rubik's 3x3x3, turn the puzzle on end so the horizontal planes correspond directly to those of a Rubik's 3x3x3 and each pair of vertical parallel diagonal planes correspond to the pairs of vertical planes of Rubik's 3x3x3; that is, this puzzle is like the Rubik 3x3x3 Fisher Cube with shaped sides. Here are photos of the other sides and how the puzzle moves:
Made in Hungary circa 1980's?
(plastic, 2 inches)
A Rubik's 3x3x3 Cube that has been beveled and employs a different color scheme; like the Pillow Cube a solution method for Rubik's 3x3x3 Cube can be used to solve this puzzle.
a.k.a. Diamond Style Puzzler
Rhombi Diamond, purchased 2007.
(plastic with tiled plastic faces, 2.3 inches)
A Rubik's 3x3x3 Cube that has been beveled like the Pillow Cube and the Hungarian Diamond but uses a simpler color scheme like the Layered Rubik's 3x3x3 Cube; same solution can be used.
This is a fun puzzle that is much easier than the standard Rubik's Cube. It has a nice feel and works very smoothly if lubricated when it is first received (in a few places use a small screwdriver in a crack to make a small opening to squirt in some silicone grease).
Note: It works just like a Rubik's Cube; you must remember to rotate layers 90 degrees at a time, even though the puzzle may look ok after a some 45 degree rotations. If the puzzle seems to be jammed and cannot rotate along a particular axis, don't worry, it is probably because of 45 degree rotations (e.g., the right side will not turn because the top and the bottom layers have been turned 45 degrees); just try some 45 degree rotations until the puzzle works again.
This puzzle was made with any of the three colors in the middle. Below are two unopend ones in the other colors, and also on the right is an earlier version of this puzzle:
Rhombi Diamond,
with orange middle.
Rhombi Diamond,
with white middle.
Diamond Style Puzzler,
circa 1980's.
(plastic with stickers, 2.1")
Further Reading
Jaap's Page, from: http://www.jaapsch.net/puzzles/diamstyl.htm
Brooks Patent, from: www.uspto.gov - patent no. 6,644,665
(This description is for top layer = white, middle layer = yellow, bottom layer = orange.)
1. Solve the middle layer.Easy if you don't care about the rest of the puzzle.2. Solve the top and bottom edges.Easy by using 180 degree front rotations to exchange incorrect edges.3. Solve the bottom back right and bottom back left corners.It is easy to play with top rotations and 180 degree front rotations to make at least one bottom corner orange; rotate this corner to the bottom back right. If the bottom back left corner is white, play some more with these rotations to make the top front left and top front middle orange, then rotate the front 180 degrees to bring these two down, and then rotate the bottom 90 degrees to bring the orange corner to the back right (and making the orange corner that was in the back right now in the back left).4. Solve the remaining incorrect corners.This can be done with just 180 degree rotations of the front (F2) and clockwise or counter-clockwise rotations of the top (U, U-). If you want to memorize a simple transformation, this one exchanges the front top left corner with the front bottom left corner:F2 U F2 U- F2
a.k.a. Magic Octahedron
Patented by C. Hewlett 1984.
(plastic, 1.8 inches between faces, 3 inches point to point,
opposite faces are green / white, yellow / blue, red / orange, magenta / gold)
This puzzle has the look and feel of a generalized Pyraminx. The rotating tips have no effect on solving (the Flowered Jewel is the same puzzle without the tips); each pyramid formed by a tip and the layer below it can rotate (this is a different puzzle than the Super Skewb Diamond). However, mechanically, the Octahedron is equivalent to a Rubik's 3x3x3 Cube without corners (or a Rubik 3x3x3 Edges Only Cube with centers) where there is one tip for each face and one face for each corner. The square on which each tip sits is the center of each face of the Rubik 3x3x3 cube and the center point of each face corresponds to a (missing) corner. The correspondence between the Octahedron and the Rubik 3x3x3 Cube may be easier to visualize by looking at the Full Octahedron which includes the centers on each face. Jaaps Page gives a direct solution.
Further reading:
Jaap's Page, from: http://www.jaapsch.net/puzzles/octahed.htm
Hewlett Patent, from: www.uspto.gov - patent no. 4,451,039
Ibrahim Patent, from: www.uspto.gov - patent no. 4,593,908
Abu-Shumays Patent, from: www.uspto.gov - patent no. 4,706,956
Made in Hong Kong, 2010.
(plastic, 1.9 inches between faces, 3.2 inches point to point,
opposite faces are green / dark green, yellow / white, blue / light blue, orange / red)
This puzzle is equivalent to the Octahedron with triangles in the center of each face and without the extra rotating tips (or a Flowered Jewel with triangles in the center of each face). It has the look and feel of a generalized Jing's Pyraminx. However, mechanically, it is identical to Rubik's 3x3x3 Cube, where each of the six points is a center square of a face of the cube, and each of the eight center triangles is a corner of the cube.
a.k.a. Jewel Puzzler, Christoph's Magic Jewel, Christoph Bandelow's Jewel
Left made in Taiwan circa 1990, right made by Mefferts 2010.
(left: plastic, 2 inches between square faces, opposite colors are
magenta / yellow, green / white, orange / red, blue / gold;
right: 2.6" between square faces, all squares are brown, opposite colors are
yellow / light blue, red / orange, purple / pink, green / blue)
Like the Octahedron, but without tips (it has the same dimensions and appears to have the same origin of manufacture). A puzzle like this but with less interesting graphics was sold as Christoph's Magic Jewel, and more recently by Meffert's as Christoph Bandelow's Jewel.
Here views of the other 7 hexagonal faces:
Patented by Erno Rubik, 1983.
(plastic, 2.5 inches diameter by 1.5 inches high;
yellow opposite green, blue opposite orange, grey opposite red;
also made in promotion versions and with six distinct pairings of the six colors;
originally packaged like a cheese, with directions on the package bottom)
A predecessor to the Rubik UFO where the two layers cannot rotate with respect to each other. Similar to a Puck Puzzle with fewer sections and without the center portion (but with the ability to flip along any of the three lines). Although this is not a trivial puzzle (harder than Rubik 1x2x2), it is not hard to solve by just playing with it. It can be solved to different color combinations (e.g., left below) and different patterns (e.g., the two on the right below). Jaap's Page presents a solution.
Further Reading
Jaap's Page, from: http://www.jaapsch.net/puzzles/kepkorong.htm
Rubik Patent, from: www.uspto.gov - patent no. 4,410,179
Made in China 2011.
(plastic, 2.7" diameter, 1.6" high;
blue top, green bottom,
purple opposite gray, yellow opposite white, orange oposite red)
Made in the theme of Rubik's Cheese but works the same as Rubik's UFO (the top and bottom layer can rotate with respect to each other). Here it is flipped over:
Distributed by Winning Moves, purchased 2005,2007.
(plastic, same puzzle with different colors, 3.25 inches)
The two types of moves that can be made are to twist by 180 degrees along one of the three axes (having the effect of exchanging three top segments with three bottom segments), and to rotate the top and bottom with respect to each other by multiples of 60 degrees. This mechanism can be viewed as a generalization of Rubik's Cheese where the ability to rotate has been added.
McFarren's Page presents a solution that first solves the top and then the bottom. Jaap's Page also presents this approach, as well as one that starts by pairing up top and bottom segments.
The opposite sides of both versions shown above are black (the green/black is translucent):
Further reading:
Jaap's Page, from: http://www.jaapsch.net/puzzles/rubufo.htm
McFarren's Page, from: http://www.geocities.com/abcmcfarren/math/ufo/ufo1.htm
Rubiks.com booklet,, from: http://www.rubiks.com/World/Rubiks%20downloads.aspx
a.k.a. Hockey Puck Puzzle
Patented by Z. Pataki, U. Mszmp, and . Csomos 1991, purchased from PuckPuzzles.com 2007.
(plastic, 2.9 inches diameter by 1 inch thick)
The outer ring can rotate around the center, and there is an axis along which two halves of the puzzle can be flipped with respect to each other. This puzzle is different, but in the theme of Rubik's Cheese Rubik's Cheese and Rubik's UFO Rubik's UFO. Jaap's Page presents a general solution, although the puzzle can be easier depending on the graphics used; here are some other examples:
Further Reading
Jaap's Page, from: http://www.jaapsch.net/puzzles/puck.htm
Smith Patent, from: www.uspto.gov - patent no. WO9,102,574
Purchased 2007.
(plastic, 4.1 inches diameter with 2.3 inch diameter center sphere)
Works the same as the Puck Puzzle but has fewer sections. Jaap's Page presents a solution and also discusses the relationship of this puzzle to the Brain Ball, Master Ball, and Top Spin.
Further Reading
Jaap's Page, from: http://www.jaapsch.net/puzzles/saturn.htm
a.k.a. Varia Disk
Patented by I. Perdy 1983.
(plastic, same puzzle with different colors, 4 inches)
The four pegs, each composed of four quadrants, can be rotated. In addition, the top and bottom halves can rotate with respect to each other, causing two quadrants of each of the four pegs to be moved to the next peg. The goal is to match each quadrant of each peg with the color on that position of the body. Each of the eight colors appears on two of the quadrants. For a harder puzzle, the two copies of each color are marked with one or two dots, and the puzzle can be solved by making the markings match as well (one dot goes to the left and two dots to the right). A newer version of this puzzle was sold as the Tricky Disky.
Further reading:
Jaap's Page, from: http://www.jaapsch.net/puzzles/tricky.htm
Peredy WO Patent, from: www.epo.org - patent no. WO83/01009
a.k.a. Tricky Disk, Mind Trapper
Patented 1989.
(plastic, 2.4 inches diameter, 3.5 inches prong to prong)
This is a later version of the Hungarian UFO puzzle that was patented in 1983 (different cosmetically, but the same puzzle). The two copies of each color are distinguished by a small circle or triangle (instead of one or two dots as in the case of the Hungarian UFO), and these same markings are on each end of the color bars on the body.
Here is a simpler three-prong version and the directions that were sold with it:
Made in China, 2007, body is 2.2 inches diameter.
Further reading:
Jaap's Page, from: http://www.jaapsch.net/puzzles/tricky.htm
International Patent, DE3,821,297.
a.k.a. Alpa-2-Go
Patented by D. Pop 1992, made by 2MUCHFUN, Bellevue, WA.
(plastic, 3 by 3 by 1.8 inches;
was also sold with a white body)
This puzzle was sold in a box where the front has a photo of the inventor and the back has a letter from the inventor and directions for use (an owners manual was also included).
Each of the four hexagons, formed from six triangles, can rotate; in addition, the upper and lower halves of the body can rotate (the puzzle works in a way similar to the Hungarian UFO and Tricky Disky, but has six triangles per hexagon rather than four quadrants per peg). When solved (as shown above), each hexagon face is one of the colors red, white, blue, or yellow, and when looking perpendicular to a face, you see the same color on the face, the top and bottom edges of the square, and the two diagonal edges of the two adjacent hexagons. This puzzle was also made with a white body and in promotional versions.
Jaap's Page presents a solution where, by reserving one hexagon for temporary use, one can solve the other three hexagons in six steps that consist of simple cycling triangles into the upper or lower half of a hexagon; then specific transformations are presented for fixing the final hexagon without disturbing the already solved three.
Further Reading
Jaap's Page, from: http://www.jaapsch.net/puzzles/alex.htm
Pop Patent, from: www.uspto.gov - patent no. 5,116,052
a.k.a. King Ring
Netblock UFO,
Patented by K. Chan 1997,
purchased from Mefferts 2006.
(plastic, 3.5 inches)
Sando Ring,
Patented by Z. Pataki et. al. 1996.
(plastic, 5.5 inches)
Each of the three balls can rotate, and so can the halves of the balls. Also, the upper and lower halves of the puzzle can rotate with respect to each other (so it is possible to mix up the eight quadrants of the three balls with each other). This is a relatively easy puzzle where you can solve one ball at a time. Jaap's Page prersents a solution.
Further reading:
Jaap's Page, from: http://www.jaapsch.net/puzzles/ufo.htm
Chan Patent, from: www.uspto.gov - patent no. 5,628,512
Pataki WO Patent, from: www.epo.org - patent no. WO96/08297
a.k.a. Meeting Colors, Disco Puzzle
Made in Indonesia and purchased in 2007.
(plastic, 5/8 diameter beads in 3.75 inch ring)
Eight beads each have 4 sections and can rotate. In addition, the upper and lower halves of the ring can rotate with respect to each other (so it is possible to mix up the 4 sections of the eight rings with each other). Similar to the Netblock UFO and Sando Rings puzzles, this is a relatively easy puzzle that can be solved one bead at a time. Jaap's Page notes that a similar puzzle is described in the patents of Ayers and presents a solution.
Further Reading
Jaap's Page, from: http://www.jaapsch.net/puzzles/octo.htm
Power Strike Page, from: http://www.powerstrike.net/puzzles/spotlight/octo.htm
Ayers Patent, from: www.uspto.gov - patent no. 4,708,345
Ayers Second Patent, from: www.uspto.gov - patent no. 4,881,738
Patented by Gerhard Huncaga 1994.
(plastic, 4.4 inches)
Each of the eight balls is split in half, and so is the main center white disk. By rotating the two halves of the disk with respect to each other, different halves of the balls can be matched up. As shipped from the factory, the blue center dial can be rotated to point the red dot to any ball, and pushing the white button in the middle of the dial causes that ball to be flipped. The puzzle can be solved one ball at a time:If necessary, use the button to make both halves of this ball you want to fix be on the top half of the disk. Rotate the bottom half counter clockwise from the position of one ball to the other. Flip that ball. Then rotate the bottom half clockwise to match the two halves. Since the bottom half was rotated the same amount in both directions, the previously solved balls remain solved, and so this procedure can be repeated to solved all the balls.In this basic factory configuration, this puzzle amounts to a simpler version of the Octo puzzle. However, the white cap of the button can be unscrewed to expose four rods with teeth that can be pulled out. In the factory setting shown on the right above, one rod (at the lower left) has been pulled out of its slot and pushed back in at the lower left corner, which causes the point of the dial that faces down to be active (rotate the ball a half turn first so after pushing in the rod it positions correctly). This can be done to any of the rods, allowing the push of the button to cause 1, 2 (at both 90 and 180 degree configurations), 3, or 4 balls at once to be flipped. The dot on each of the four points of the dial (on both sides) can be rotated between blue and red to remind you of which points are active. Do all of this with the puzzle in the solved state (since not all positions are reachable in other settings). Jaap's Page gives solutions for all other settings.
Further Reading
Jaap's Page, from: http://www.jaapsch.net/puzzles/gerdig.htm
Gerhard Patent, from: www.uspto.gov - patent no. 5,370,394
Patented by A. Unsicker 1999.
(plastic, 3.5 inches, the back side of each number is white)
Numbers are yellow on one side and white on the other, and can rotate any number of positions in either direction. In addition, there is a north pole that spans three numbers (13, 1, 2 in the photos above) and a south pole that spans four numbers (6, 7, 8, 9 in the photos above); a flip turns these 7 numbers along the pole axis:
->
Solution: Use ideas from Jaap's Page (which also presents moves to speed up solving). For a positive integer n, n and -n denote clockwise and counter-clockwise rotations by n positions, and / denotes a flip. The pole position P is the center of the north pole, and the two positions to its right clockwise are Q and R.
Step 1: Make the side facing you all yellow by using as needed:2/-2/2/-2 = flip the pole positionStep 2: From 1 to 11, move counter clockwise to its position, using:1/-1/6/-6/-6/-6/-1 = PQR -> RPQStep 3: If 12 and 13 are reversed, change parity by changing the side facing you from yellow to white (which mixes the numbers) turn over the puzzle, and repeat Steps 1 and 2:
That is, repeatedly move the next piece to position R and use this transformation to advance it two positions towards its goal. If it is only one position away, first advance number to its right./5/5/ = flip all of the numbersFurther reading:
Jaap's Page, from: http://www.jaapsch.net/puzzles/brain.htm
Unsicker Patent, from: www.uspto.gov - patent no. 6,003,868
K8 Ball
(plastic, 3.25 inches)
A Rubik's 2x2x2 with a smooth internal mechanism patented by S. Khoudary 2000. It has been made with different graphics besides the "K8" graphics shown on the two balls above; here is an example:
Ying-Yang Ball
(plastic, 3.25 inches;
on one section "K-Ball" is molded into the plastic near the point
and near the opposite side of that section,
"World Patents WO0025874 Made in China")
Further reading:
Khoudry International Patent, IP25874.
Works like a Rubik's 3x3x3.
(plastic, left 3 inches, right 3.5 inches)
Made in China, 2010.
(plastic, 2.8 inches wide, 3" high with stem)
Mechanically, the same puzzle as the standard Rubik 3x3x3, and any solution for that puzzle can be used, but here it is the shape that gets mixed up rather than the color.
a.k.a. Duo Master
Patented by Geza Gyoval 1989.
(3 inches)
The three basic moves are a north or south pole 45 degree turn, an equator 45 degree turn, or one of the four longitude 180 degree turns. Solve the rest of the puzzle first and then solve the poles by interleaving pole turns with pairs of longitude turns; or, solve the poles first and then as you do the rest maintain the poles solved (or in solved halves that can be fixed at the end). The NS pattern, where the top half is white and the bottom half black, is easy to visualize and not hard to do once you have worked with the puzzle a bit.
From NS, one longitude turn followed by one equator 180 degree turn gives EW:
From EW, the following sequence gives a rectangular checkerboard:
Or, the use four steps to get the "slice" pattern, and one more to get the "checkerboard":
Like the standard Master Ball, except with stars on one pole (has no significant effect on solving) and the letters U, S, A on three of the center white tiles. Two possible solutions are shown below. On the left is the slice pattern (the A is on the next white slice to the right of the S), on the right is the NS pattern, and in the middle is a pattern than can be used to go from the left to the right, as described below.
Solving the slice pattern with letters arranged:Solving the NS pattern with letters arranged, method 1:
- Ignore letters and solve checkerboard as for the standard ball.
- With the checkerboard pattern, longitude 180 degree turns and equator 90 degree turns preserve the checkerboard pattern; so it is easy to permute the center white tiles to put the U, S, and A tiles where ever you want.
- Do a 45 degree equator turn to restore slices, and fix the poles.
Solving the NS pattern with letters arranged, method 2:
- Starting with the slice pattern, rearrange the letters (using step 2 of the slice pattern solution above) to the position shown in the middle photo above.
- Reverse the NS to slice pattern transformation of the standard master ball by starting with the U to the left of the plane used for the first longitude turn.
NOTE: For a different transformation for slice to NS, the correct starting position can be determined by marking the center white tiles and seeing where they go when you do your transformation.
- Ignore letters and solve NS pattern as for the standard ball.
- Jaap's Page gives the transformation below to exchange two tiles, which can be applied repeatedly to rearrange the center white tiles as needed; a vertical arrow is a longitude rotation and a horizontal arrow an equator rotation:
Once solving the standard and USA versions has been mastered, this is not too much harder. Again, poles can be solved separately. Then, one approach is to get the top and bottom halves to each have one of each color, and then use method 2 for the USA Masterball (which also has the effect of exchanging two bottom tiles) to make tiles to line up from top to bottom.Other Versions of Master Ball
a.k.a. Geo Master
The Master Ball has been made (with the identical size and mechanism) with many different graphics (Circus Master, Dragon Master, Soccer / Football Master, Tennis Master, Cat Master, WWF, etc.), including promotional versions (e.g. Paramount Pictures IQ), making the puzzle a bit harder than the rainbow version by making all sections unique. Jaap's Page presents a general solution.
Circus Master
Soccer Master
Further reading:
Jaap's Page, from: http://www.jaapsch.net/puzzles/master.htm
Gyoval Patent, from: www.uspto.gov - patent no. 4,856,786
a.k.a. Creative Puzzle Ball
Patented by U. Meffert 1994; purchased from Mefferts.com 2005.
(plastic, 3 inches, keychain is 1.5 inches)
This puzzle rotates about the center along 4 different planes that partition the surface into 8 triangles and six squares. Rotation has click stops but is not symmetric in that if you split a ring in half by turning half the puzzle 180 degrees, you don't end up in a click stop. Internally, it uses a mechanism equivalent to the skewb cube. Here's what Meffert's says about the puzzle:
"The 3-D Puzzle Ball moves a group of three squares and four triangles through 120 degrees by rotating around the triangle at the center of the group. It has precision injection moulded parts with spring-loaded bearings which make operation easy and exact; this is a puzzle which definitely won't fall apart in your hands. The idea of the puzzle is to scramble the colors and then return them to the initial state. You may also want to make pretty patterns with it as well though. The Beach Ball Puzzle is difficult enough to be a real challenge, but easy enough to master, without help, in a few days. Just in case you do have difficulty in solving the Puzzle, a solution booklet is included with the puzzle."
Further reading:
Jaap's Page, from: http://www.jaapsch.net/puzzles/beachbll.htm
Meffert's Page, from: http://www.mefferts.com/puzzles/creasol.html
Meffert Patent, from www.uspto.gov - patent no. 4,474,376
Meffert's Black Creative Puzzle Ball, 3" |
Meffert's Beach Ball, 3" |
Meffert's Mickey / Donald Ball, 3" |
Meffert's Mickey / Goofy Soccer Ball, 3" |
Meffert's Bugs Bunny / Pluto, 3" |
Meffert's Sega Ball, 3" |
Baseball made in Hungary 1980's, 2.75" |
Zodiac ball made in Hungary 1980's, 2.75" |
Hungarian Air Promotional 1980's, 2.75" |
a.k.a. Incrediball
Patented in 1984 by William O. Gustafson and others;
purchased from Mefferts.com.
(3 inches)
Each of the groups of five triangles can rotate (it doesn't look like they should be able to, but there is a spring mechanism that lets them flex up enough to rotate). The groups intersect in twelve circles. In the solved state, there are six distinct circle colors, where each circle has the same color as the one opposite it. Jaap's Page notes that this is the same puzzle as the Kilominx, and presents a solution.
Further reading:
Meffert's Page, from: http://www.mefferts.com/puzzles/impossol.html
Jaap's Page, from: http://www.jaapsch.net/puzzles
Gustafson Patent, from www.uspto.gov - patent no. 4,474,376)
Blazek and Jandora Patent, from www.uspto.gov - patent no. 6,994,343)
Djukic DE Patent, from: www.epo.org - patent no. DE20211793
Djukic WO Patent, from: www.epo.org - patent no. WO03105978
Obermair DE Patent, from: www.epo.org - patent no. DE3204033
Patented by Zoltan and Robert Vecsei 1993, purchased from Mefferts 2007.
(plastic, 3.5 inches)
This puzzle has twenty faces that meet at 12 vertices. Mefferts has made this puzzle in a number of color schemes, including the 12 color "Dogic 1" (on the left above) where each vertex is colored, the 10 color "Dogic 2" (on the right above), where each face is colored (and each color appears on two of the 20 faces), the 5 color "Dogic 3", the 2 color "Dogic 4" and "Dogic 5", and the 20 color "Dogic 6". A set of 5 faces can be rotated about a vertex, or just the five triangles that meet at a vertex can be rotated.
Here are what a few moves of Dogic 1 look like:
Here are what a few moves of Dogic 2 look like:
Jaap's Page gives a solution that solves one tip at a time, and then uses the solution for the Impossiball to solve the faces.
Further Reading
Meffert's Page, from: http://www.mefferts.com/solution/dogic/dogic_solution.htm
Jaap's Page, from: http://www.jaapsch.net/puzzles/dogic.htm
Vecsei HU Patent, from: www.epo.org - patent no. HU214709
a.k.a. Magic Octagonal Prism, The Octagon, The Barrel
P.G. CO, circa 1980's.
(left plastic 2.2 inches, right metal ring and plastic 1.25 inches)
This is the same as Rubik's 3x3x3 Cube with the corners beveled along the vertical dimension, and the same solution can be used. However, as shown below, it can look like a bit of a mess and, as explained on Jaap's Page, Jaap's Page, you may have to flip a single edge by flipping it and a beveled one, or exchange two pieces by exchanging them and also a pair of beveled ones.
Further Reading
Jaap's Page, from: http://www.jaapsch.net/puzzles/barrel.htm
Same puzzle as the standard 3x3x3 Rubik's Cube.
(plastic, 2.2 inches)
This puzzle is shaped like the Rainbow Cube (a cube with the corners cut off); there are six square faces corresponding to the faces of a cube (colored green, blue, light blue, orange, yellow, and white) and eight triangular faces corresponding to the corners of a cube (colored red, green, gold, purple, grape, pink, white, and cream). However, the operation of this puzzle is different. Here, a layer parallel to a square face can rotate, and a solution for a standard Rubik's 3x3x3 Cube can be used.
Further Reading
Wikipedia Cuboctahedron Page, from: http://en.wikipedia.org/wiki/Cuboctahedron
Purchased from PUZL.co.uk 2007.
(plastic, 2.25 inches)
This puzzle is shaped like the Cuboctahedron (a cube with the corners cut off); there are six square faces corresponding to the faces of a cube (opposite pairs are colored red, yellow, and orange) and eight triangular faces corresponding to the corners of a cube (opposite pairs are colored green, blue, light blue, and purple). However, the operation of this puzzle is different. Here, triangular faces (formed from 4 little triangles) can be rotated.
Jaap's Page gives a solution, notes that this puzzle has eight axes of rotation like the Skewb, and discusses the relationship of this puzzle to the Dino Cube, Brain Twist, and Platypus.
Further Reading
Jaap's Page, from: http://www.jaapsch.net/puzzles
Made in Hungary, circa 1980's?
(plastic, 2.25 inches across minimum dimension, 3.5 inches across farthest points;
white body with colors red, light blue, dark blue, green, yellow, brown, gray, black;
the same puzzle was also made with different color schemes,
including orange, yellow, red, blue, and green bodies)
Each of the six points can rotate, and the object is to make a circle of the same color on each of the six faces on which the points sit.
This puzzle is commonly referred to as the "Dino Star" because it is logically the same puzzle as the Dino Cube. Each of the six points corresponds to a corner of the Dino Cube. When a point rotates, 3 pairs of colors move. For example, looking at the photo above, when rotating the forward facing point, the circle of red rotates, and as it does, the red and blue segments rotate together (as do the other two red segments with the two other colors that cannot be seen in the photo). These pairs of colors that move together correspond to the pairs of triangles that move together on the Dino Cube (a total of 12 pairs in either puzzle). To color the Dino Cube to be like the Dino Star, start with a blank cube and draw a circle of a unique color around each corner; the result will be each triangle pair having two different colored arcs on it:
->
a.k.a. Other Name
Patented by Adam Alexander 1985, made by Ideal Toy Co. 1992.
(plastic, 3.5 inches)
Each point can be rotated around the plane perpendicular to it. The solved state, as shown in the photo above, is when each pair of parallel planes is the same color. Jaap's Page mentions the relationship of this puzzle to the Megaminx and presents a three step solution, where the first step uses only two simple trnsformations to solve everything except the five pieces around one vertex, the second step positions the edges of this final vertex using one of five transformations, and the final step employs two transformations to orient these edges.
Further Reading
Jaap's Page, from: http://www.jaapsch.net/puzzles/alexandr.htm
Alexander Patent, from: www.uspto.gov - patent no. 4,506,891
Nieto Patent, from: www.uspto.gov - patent no. 4,500,090
a.k.a. Jackpot
Patented by Seyhan 2006, purchased from Mefferts 2007.
(plastic, 4.5 inches;
both have tips A, K, Q, J and faces clubs, diamonds, hearts, spades;
a "collectors" version on right has faces colored green, yellow, red, blue)
Both the tips and faces can be rotated:
Jaap's Page presents a solution and relates it to that for the Dino Cube, Rainbow Cube, and Brain Twist. Mefferts has made a number of versions of this puzzle and gives four challenges for the Jackpot version that is shown on the right above:1. Match all four card suites on each side.Mefferts has sold other "collectors" versions, and also versions with electronics where lights go on when a side is solved.
2. Match the same 3 outside card suites to different card suite centers.
3. Line up all the J (Jacks) Q (Queens) K (Kings) and A (Aces) on each of the 4 apex columns.
4. Line up the matching color bars in 6 locations around the center core.
Further Reading
Jaap's Page, from: http://www.jaapsch.net/puzzles/dinocube.htm
Mefferts's Page, from: http://www.mefferts.com/solution/jackpot/index.html
Seyhan International Patent,, WO03/004117.
a.k.a. Golden Egg, Silver Egg, etc.
Designed by Tony Fisher, purchased from Meffert's, 2009.
(plastic with metallic finish, 4.25 inches high by 3 inches diameter;
left "Golden Egg", middle "Golden and Silver Egg", right "Silver Egg";
also made in gold+silver, copper, white, red, green, blue, and yellow)
Like the Golden Cube, uses a Skewb mechanism and has a shiny metallic finish, and in the same spirit as the Rubik 3x3x3 Mirror Block pieces of the cube are distinguished by shape rather than color. In fact, the shiny surface combined with the egg shape make this puzzle almost like a fish eye lens when photographed (one can see the photographer and much of his kitchen in the photos above).
Patented by C. Hoberman and M. Davis 2005, made by Hoberman Designs.
(plastic, each edge of the pyramid shape is 4.75 inches)
Below are the directions that came with the puzzle. Jaap's Page presents a solution and relates it to that for the Dino Cube, Rainbow Cube, Platpus.
Further Reading
Jaap's Page, from: http://www.jaapsch.net/puzzles/dinocube.htms
Hoberman and Davis Patent,, from: www.uspto.gov - patent no. 7,125,015
Patented by F. Gruber 1993, Copyright Interconcept GmbH.
(left: plastic, 3 inches, 3-wing version, red / blue / yellow;
right: plastic, 4-wing version, black / white / blue / green / red / yellow / gray / purple)
The basic operation is to make two of the semi-circles co-planar and then rotate the resulting circle 90 degrees. After mixing up, restore the puzzle to a fun pattern. Below are the directions that were sold with the 3-wing version. Jaap's Page presents a solution.
Further Reading
Jaap's Page, from: http://www.jaapsch.net/puzzles/roundy.htm
Gruber Patent, from: www.uspto.gov - patent no. 5,267,731
There are many puzzles that are not of the same general form as Rubik's Cube, but are in the same theme of a manipulation puzzle (often quite hard) that you can pick up, play with, and put down unsolved without being stuck with a bag of pieces.
a.k.a. Rubik's Magic Junior
Wallace and Gromit, made by A. R. Mason, U. K. 2007.
(plastic, four 2" panels held by wire loops, when front is solved, back is not)
The smallest of the Rubik magic panels puzzles. There are four ways to fold the puzzle in half; as shown in the directions to the Rubiks Magic Junior Picture Game series (see the next page), two of these let you do the loop transform (also called the roll) and two the star transform. By learning what they do, the puzzle can be solved very quickly, or by just more or less randomly playing with them, the puzzle usually solves without too much effort.
Further reading:
Jaap's Page, from: http://www.jaapsch.net/puzzles/magicmini.htm#desc
This series of four puzzles, made by matchbox 1986 (plastic, four 2" panels), each has mice, so that the four can make a larger scene of mice. The opposite sides with backgrounds of yellow, brown, green, and blue, have cute characters that can be arranged in a number of ways.
Rubik Studio Promotional Mice Theme 1985 (Hungarian).
(plastic, 2" panels, both sides always look solved;
shown is the position when the text runs along the bottom)
Rubik Studio Promotional Fantasy Theme 1988 (Hungarian).
(plastic, 2" panels, when front is solved, so is back)
Kellogg Promotional 1988.
(plastic, 2" panels, the little top center left triangle on the front side has been repaired,
"RUBIK/RUBIK'S MAGIC TM PROP OF 7 TOWNS LTD PATENT APPLIED FOR
C 1988 KELLOGG COMPANY MADE IN CHINA")
Hungarian Malev Airlines promotional 1989, Buda Castle on the back.
(plastic, 1.5" panels, front and back not solved at the same time)
Hungarian Malev Airlines promotional 1989.
(plastic, 1.5" panels, when front is solved, back is not)
Hungarian Apisz Promotional 1986 (paper and accessories store).
(plastic, 2" panels, when front is solved, so is back)
Scooby Doo, www.rubiks.com, circa 2000.
(plastic, 2" panels, when front is solved, back is not)
Simpsons, made by A. R. Mason, U. K. 2007.
(plastic, 2" panels, when front is solved, back is not)
England tourism promotional, made in the U.K 2007.
(plastic, 2" panels, when front is solved, back is not)
Patented by E. Rubik 1987-U.S. & 1985-Hungary.
(plastic, eight 2" panels, original black panels and newer red panels)
Eight panels, held by wire loops, can be folded and manipulated. Mix up and restore the 2x4 solution of 3 rings, or make the reverse side 3x3 (with a missing panel) solution of 3 linked rings. It is also fun to make different 3D shapes.
The star transform of Rubik's Magic Junior can be generalized, the Rubik's Magic directions show a generalized loop (called roll) and three new ones:
star transform:
Note: If in Step 3 of the wallet stack
you pull it apart horizontally
instead of vertically, you get the
"row swap transform"
(see Jaap's Page) that exchanges
the top and bottom rows.
After mixing up the puzzle, simply playing with the basic transformations typically gets you back to the starting pattern of three disconnected loops, and the more you do it, the more you get an intuition on how to do it faster. At some point, it is useful to really think about what each transformation does. Below, on the left is shown the starting position with panels labeled from 1 to 8 (or the back of the starting position with panels labeled A through H). The right shows where each panel goes; bars indicate where the top of that panel is now positioned.
The basic transformations together with the two hints of the red panels directions shown above lead to the following solution. Some other versions of the puzzle (e.g. Simpson's and Harry Potter) have the graphics placed so that this solution works.
0. If necessary, as per Hint 1, play with transformations to restore the 2x4 solution; if using the new red version, reposition it with the copyright at the top (text upside-down).
1. As per Hint 2, do a reverse, and then position the puzzle horizontally (where the upper right three panels are are the lower right three panels of the linked solution):
2. Continuing as per Hint 2, do a half roll towards the left that moves the upper right three panels to the lower left (when you are done, the underside has the pattern shown in Hint 2):
3. Do the transformer:
Jaap's Page credits the following method to Alexander Oohms.
0. If necessary, play with the transformations shown in the puzzle directions to restore the puzzle to the 2x4 solution.
1. Fold the right two panels up and then fold lengthwise:
2. Arrange into a 2x1 box where the right side is two panels thick, fold the extra two panels up through the box and back down (so they are now on the outside right), and then push the right side in to make a stack of 6 panels:
3. Push the stack of 6 down so that you have an open half box with a bottom that is 2 panels thick, flip the extra 2 panels under the bottom around 180 degrees to lie flat, and then rearrange into a Z shape:
4. Flip down the extra two panels on the back of the top of the Z (so the center of the bottom row is now three panels thick), flip the third center panel to the left so that all three sections of the bottom row are now two thick, then flip the extra row of three on the bottom down:
New orange version, 2" panels, same as new red one.
Simpsons, 2" panels.
Harry Potter, 2" panels.
Porsche / Mercedes, 1.5" panels.
Mini Dinosaurs, 13/16" panels (really small but it works).
Further Reading
Jaap's Intro, from: http://www.jaapsch.net/puzzles/magic.htm
Jaap's Transforms, from: http://www.jaapsch.net/puzzles/magictrn.htm
Jaap's Solutions, from: http://www.jaapsch.net/puzzles/magicstd.htm
McFarren's Page, from: http://www.geocities.com/abcmcfarren/math/rm1/rm1int.htm
Koller's Page, from: http://www.mathematische-basteleien.de/magics.htm
Garron's Page, from: http://cube.garron.us/magic.htm
Rubiks.com booklet, from: http://www.rubiks.com/World/Rubiks%20downloads.aspx
Rubik Patent,, from: www.uspto.gov - patent no.4,685,680
Same mechanism as the standard Rubik's magic panels.
(plastic, eight 2" panels)
This puzzle works the same as the standard Rubik's Magic, and the same transformations can be used (star, roll, reverse, wallet stack, transformer, etc.). On the top side (shown above) all panels the same green, red, blue, yellow clockwise pattern. On the bottom side, all panels have the same 4 colors, but not all in the same order.
The goal is to make a cube sitting on a 2 panel base; this can be done with the standard Rubik's magic as well, but here the graphics allow for two nice looking solutions with matching colors at the corners. The "horizontal" solution shown above has the text horizontally on the side and the "vertical" solution used to illustrate the solution steps on the next page has the text going vertically on the side.
Further reading:
Jaap's Page, from: http://www.jaapsch.net/puzzles/magiccrea.htm#desc
We illustrate one of the solutions presented on Jaap's Page that makes use of a box and lid construction in the flavor of Ooms method for the standard Rubik's Magic solution.
0. With the bottom side facing up, manipulate the puzzle using the standard transformations to have the arrangement on the left (which leads to the horizontal solution) or the arrangement on the right which leads to the vertical solution (which we use for the illustrations below). One can go between these two arrangements with a standard right roll transform.
1. Flip the left two panels up an over, fold lengthwise, arrange into a box, fold the extra two panels on the right up and down into the box so now they are in the inside of the right:
2. Rearrange to three long with a stack of 4 on the right, fold the back right panel left to the middle, and fold up the front three:
3. Hold the left two panels with your left hand (don't let go until this step is completed), pull up the middle pair of panels up with your right hand to make a box, flex the left two panels to fold together towards you and use your right hand to guide the formation of the box, then unfold the two panels still in your left hand to make the base for the cube:
Left top original made by Matchbox 1987, left bottom newer black version.
(plastic, twelve 2" panels)
This puzzle works the same as the standard Rubik's Magic, and the same transformations can be used (star, roll, reverse, wallet stack, transformer, etc.). The goal generalizes the standard Rubik's Magic Panels to make a W shape on the back with the 5 rings unlinked. The puzzle directions also show many 2D shapes that can be made:
Further reading:
Jaap's Intro, from: http://www.jaapsch.net/puzzles/magic.htm
Jaap's Transforms, from: http://www.jaapsch.net/puzzles/magictrn.htm
Jaap's Solutions, from: http://www.jaapsch.net/puzzles/magicmast.htm#desc
Jaap's Page credits the following solution to C. McFarren, which reduces the solution to two applications of the standard Rubik's Magic transformer transform. The illustration below is for the original silver version; the newer black version also shown shown on the previous page works exactly the same (although Jaap's page notes that some of these puzzles have graphics placed in a way that a mirror image solution us used).
0. Do a roll to the right:
1. Flip the left and right two panels up an over, flip the upper left and upper right top panels towards you, fold the left two and the right two up and over towards the center to form an upside-down T, then fold the bottom upper two up and back to length the stem of the T:
2. Roll the base of the T one panel to the right and then fold out the bottom 4 from underneath to form a reverse L shape:
3. Do the standard Rubik's Magic transformer transform on the top of the L (note that for the second step, the panel flips to the left):
4. Do the standard Rubik's Magic transformer transform on the leg of the L (note that for the second step, the panel flips upward):
Left made by V.V.V. Puzzle 1987, right made by CN Studio and purchased 2007.
(plastic, twelve 2" panels)
Twelve panels, held by wire loops (length and confoguration differs from Master Magic), can be folded and manipulated. To change the back side to a cross:
0. If necessary, use basic transformations (as for Master Magic) to restore the 2x6 solution. For the black version, turn puzzle over (V.V.V at the top, upside-down).
1. Fold the top half down, rotate right two panels, and unfold:
Note: For the black puzzle, you instead roll to the left, to end up with:2. Fold each end over, fold at the middle, split each side and fold together, fold the two 2x2 sections down, and then unfold the left and right portions of the cross:
3. It is now solved on the other side (for the black, you don't need to turn it over).
Further reading:
Jaap's Page, from: http://www.jaapsch.net/puzzles/magicrings.htm#desc
Upper left is the "standard version", upper right has different background color,
bottom two have 4 chess square per tile, all purchased in 2005.
(plastic, sixteen 2" panels)
This puzzle works the same as the standard Rubik's Magic Panels, and the same basic transformations can be used (star, roll, reverse, wallet stack, transformer, etc.) to make many different 2D and 3D shapes. Jaap's Page shows how to solve the back to a big W shape with five balls on it. It can easily be made into 4x4 panels; for the chess versions that have 4 chess squares per panel, it can be a fun challenge to rearrange the 2x8 shape, and then see what chess position results on the (front or back) of the 4x4 shape.
Further reading:Jaap's Intro, from: http://www.jaapsch.net/puzzles/magic.htm
Jaap's Transforms, from: http://www.jaapsch.net/puzzles/magictrn.htm
Jaap's Solutions, from: http://www.jaapsch.net/puzzles/magicsuper.htm#desc
Twisty Puzzles build info, from: http://twistypuzzles.com/articles/magic-super-master.shtml
a.k.a. Genius Puzzle
(3 section, 6 column tower is 1.75" by 2.75" long with 5/8" tiles,
3 section, 6 column Genius tower is 1.75" by 2.8" long with 5/8" tiles,
3 section, 6 column keychain tower is 1.75" by 2.75" long with 3/4" tiles,
2 section, 6 column custom made tower is 1.75 inches by 2" long with 3/4" tiles
4 section, 6 column keychain tower is 1.25" by 3" long with 1/2" x 3/8" tiles,
4 section, 6 column keychain tower 2 is 1.25" by 2.25" long with 3/8" tiles,
6 section, 6 column tower is 2" by 4.75" long with 3/4" tiles)
These puzzles consist of a number of sections that can rotate; the puzzle is solved when each column has a single color. One color has one fewer tiles than the others, and this gap is what allows pieces to be moved around. Because all tiles of a given color are identical, solving is relatively easy; any tile can effectively be moved to any position without disturbing the others, with any assignment of colors to columns, one tile at a time (larger versions just take longer). When the number of number of sections and columns is the same, a second problem is to put the same color tile in each row.
When the number of number of rows and columns is the same, a second problem is to put the same color tile in each row.
Further reading:
Jaap's Page, from: http://www.jaapsch.net/puzzles/tower.htm
(plastic, 6 columns,
(4 section, 4 column tower is 1.4 inches by 3.5 inches long with 5/8" dia. balls,
4 section, 4 column key ring tower is 5/8" by 1.75" long with 3/16" dia. balls,
5 section, 5 column tower is 1.6 inches by 4 inches long with 5/8" dia. balls,
7 section, 7 column tower is 1.6 inches by 4 inches long with 3/8" dia. balls)
This puzzle is slightly different from the Whip-It Towers in that instead of one column missing a ball to create the gap, there is an extra section that has the gap. However, just like the Whip-It towers, any ball can effectively be moved to any position without disturbing the others (given that all balls of a given color are equivalent), and these puzzles can be solved in any order (with any assignment of colors to columns) one ball at a time (it just takes longer when there are more columns and / or sections). In fact, if you first just park one of the balls in the gap, then this puzzle is identical to the Whip-It Towers, except at the end you just drop the ball on on the appropriate column.
Because the number of rows and columns is the same, a second problem is to put the same color ball in each row.
Further reading:
Jaap's Page, from: http://www.jaapsch.net/puzzles/tower.htm
The Smaries tower is identical to the standard 4 section Varikon tower except for color and the addition of the text at the bottom "Smarties Smarties Smarties Only Smarties Have The Answer". It comes with directions that frame it as a game with a number of things to do.
Purchased 2008.
(material, 3.5 inches)
A slightly easier version of a Whip-It Tower puzzle, where pairs of columns have the same color. Here is a photo fo the other side:
a.k.a. Ivory Tower
Patented in 1982 "Arxon Speil + Freizeit GMBH", made by Ideal Toy Co.;
Jaap's Page credits design to Endre Pap, who designed the Hungarian Rings.
left: 5 sections, 6 cols., 1.9" base, 1.6" top, 3" long, 7/16" dia. balls;
middle: 6 sections, 6 cols., 1.9", 1.6", 3.5" long, 7/16" dia. balls;
middle: 7 sections, 6 cols., 1.9" base, 1.6" top, 3.9" long, 7/16" dia. balls
Go from darkest to lightest color type in each column (red, blue, green, yellow, brown, gray). Different from Whip-It Towers and Varikon Towers; instead of a gap, there is a spring between two of the bottom balls that allows one to be pushed in so that the ball above it can drop down. This solution based on Jaap's Page:Further reading:
- Make each column have the same color type: Push one ball in to create a gap and then proceed as for Whip-It Towers and Verikon Towers (i.e., when all shades of a given color are equivalent, you can essentially use the gap to move any piece where you want to).
- Place all but the top two balls of each column: If XYZ are three consecutive balls in a given column, by making a gap in a column next to it, you can do XYZ -> YZX -> ZXY, and thus X can be moved down 2 sections, or Y can be moved down one section. With this trick, all columns can be ordered correctly except possibly for the top two sections.
- Fix parity if necessary: If an odd number of columns have the top two balls out of order, then rotate the top layer one position and repeat Step 1 on the top two layers only (so that the top two layers have the same color type as the already solved lower layers).
- Work two columns at a time to fix the top two layers: Pairs of columns that have the top two balls out of order can be fixed with the following nine step transformation that manipulates 6 balls; the top two balls and the gap are denoted A, B, #, and the balls initially below these three positions are denoted X, Y, Z. In this figure, columns are shown next to each other, but they can be anywhere, and the top two layers are always shown rotated so that the 6 balls being manipulated are together:
Step 1
AB#
XYZStep 2
ABX
#YZStep 3
A#X
BYZStep 4
AYX
B#ZStep 5
AY#
BXZStep 6
AYB
#XZStep 7
#YB
AXZStep 8
XYB
A#ZStep 9
XY#
ABZ
Babylon Towers Directions.
Jaap's Page, from: http://www.jaapsch.net/puzzles/ivory.htm
Babylon Towers DE Patent, from: www.epo.org - patent no. DE3104021
Circa 1990?
(plastic, 2.75 inches across by 3.5 inches high inches)
The numbers 1 to 31 are arranged in 7 columns of colored tiles (6 red, 6 yellow, 6 purple, 6 green, 6 orange, 6 blue, and 5 white), and the goal is to put the days of the month in increasing order going clockwise and down. Similar to the Babylon Towers, and a similar solution can be used, although this puzzle is easier because there are two blank tiles at the bottom of the green, orange, and blue columns.
a.k.a. Clever Toys Tower
Purchased by J. A. Storer in Bangkok 2008, this puzzle also sold by Clever Toys.
(wood, 2.9"x4.1", five each red, blue, green, and yellow 9/16 inch diameter balls)
There are four columns, which when solved, each have 5 balls of the same color. The ends cannot rotate; one has a single receptacle that can hold one ball and the other has one receptacle for each column. Harder than the Varikon Towers, but easier than the Babylon Towers.
Solution: It is convenient to think of the bottom as the end with the single receptacle and the top as the one with four receptacles, and to work from the bottom up in three steps:1. It is easy to place the bottom balls (it doesn't matter how you mix up the remainder of the puzzle).
2. The second and third rows can be fixed in a manner similar to the Varikon Towers (they are adjacent to the center by which the rings rotate).
3. The top two rows are adjacent to the top edge of the center ring and can also be solved in a manner similar to the Varikon Towers.
Made in Hungary circa 1980's?
(plastic, 2.2 inches diameter by 2.9 inches long inches)
Tiles are numbered 1 through 6 in red, 7 through 12 in yellow, 13 through 18 in blue, and 19 through 23 in green. Tiles can rotate around the barrel in each of the three loops. Tiles can also move between loops in two positions (in the photo above, between positions 4 and 12 and between 16 and empty position 24). The numbers can easily be arranged in any order in a spirit similar to but even easier than the Fifteen puzzle.
Patented in 1981 by S. Hanson and J. Breslow.
(plastic, 1.5 inches square by 5 inches long;
deluxe version has same size / end labels / directions, and
although photos do not show it well, it has chrome rings on all sides;
keychain version is plastic 5/8 inches square by 2.25 inches long)
A piece can slide into the empty slot and the puzzle can twist at the end sections, but not the middle. It is easy to solve the yellow and green columns (or any two of the non-white colors), and then the red and white can be solved without disrupting the already solved columns, where the basic operations are cycling 5 pieces (all but the top of one column and the bottom of the other or vice-versa), or cycling 3 pieces at one end of the puzzle or the other.
This puzzle is harder than a 4-high Whip-It Tower because you can't rotate at the center (solving the last two columns by cycling pieces is more like a 3D version of the Fifteen puzzle).
Below are the instructions that came with it:
Further reading:
Jaap's Page, from: http://www.jaapsch.net/puzzles/missing.htm
McFarren's Page, from: http://www.geocities.com/abcmcfarren/math/rdml/rubmlk0.htm
Below are the other two sides and end stickers of the Missing Link and Missing Link Deluxe, and the other two sides of the Missing Link keychain (the keychain does not have stickers):
There are other productions of this puzzle; some the same but with different stickers (e.g., one sold in France said "Le Chainon Manquant" on the stickers), as well as ones that have the same dimensions but different colors, different internal construction, or different overall quality. Here are three examples of different ones with English language stickers; for all three, the stickers on the two ends are the same:
Made by Mariusz Dabrowski, 2007.
(plastic, 1.5" square, 3.8" long)
Custom made by replacing the double center portion of a standard Missing Link puzzle by a single section. This makes a puzzle equivalent to the (much easier) 3-Section Whip-It Tower.
This particular puzzle has solid ends with no holes or exposed parts (so stickers are not required on the ends to cover anything up) and a very smooth click-stop action. Here are what the other two sides and other end look like:
Made by Mariusz Dabrowski, 2007.
(plastic, 1.5" square, 6.1" long)
Custom made by extending the center portion of a standard Missing Link puzzle from two to three sections (using parts from two puzzles) in such a way that these three sections cannot rotate with respect to each other (so like the standard Missing Link puzzle, only the two end sections of the puzzle can rotate). This extension does not change the basic complexity of the puzzle; it can be solved the same way as the standard version (and this remains true for an number of extensions of the middle).
This particular puzzle has solid ends with no holes or exposed parts (so stickers are not required on the ends to cover anything up) and a very smooth click-stop action. Here are what the other two sides and other end look like:
Made by J. A. Storer, 2007.
(plastic, 1.5" square, 7.1" long)
Custom made by adding a second double center portion to a standard Missing Link puzzle (using parts from three puzzles). Some 6-section Missing Link puzzles have been made where all four center sections are joined (so that the puzzle only rotates at the ends), but this is just a longer version of the Extended Missing Link puzzle (and is not any harder). This Doubled Missing Link puzzle can rotate in three places (the two ends and between the two double center portions), and so is a new puzzle that is a bit easier than the standard or extended versions, but still harder than the reduced version or a Whip-It Tower puzzle.
Here are what the other two sides and other end look like:
The central spindle may differ between different Missing Link puzzles. The most common version that was sold in the U.S. has a solid plastic center spindle with bumps on it; start by getting three of one of these:
After removing the stickers (save them), one end cap, call it the bottom, has a recessed hole in which sits a flat end of the spindle, and in the other end, call it the top, the spindle comes to a point and locks with two prongs into a smaller hole.
Take apart three Missing Link puzles. Force the top end off (ok if it breaks, it won't be used), slide off the sections, and slide the tiles out of the sections. All of the sections are identical; each has a locking side and free side (when two locking sides face each other, those two sections cannot spin with respect to each other).
Find a metal rod that has a diameter to match the holes in the sections, line up on the rod a bottom end, six sections, and a second bottom end, and mark where to cut so the length of the rod will be slightly shorter than the distance between the insides of the recessed holes of the end caps. Then drill and tap a 5/8 inch deep 6-32 threaded hole into each end of the rod (easiest to drill the holes on a lathe, and you can also use the lathe to face off the ends of the rods). The head of a 6-32 screw and a washer will fit in the recessed bottom end cap holes.
Screw one end cap on tight with a 1/2" 6-32 screw and washer. Add the 6 sections where the locking side of section 1 faces the cap, the locking sides of sections 2 and 3 face each other, the locking sides of sections 4 and 5 face each other, and the locking side of section 6 faces the other end cap. As you are adding caps, add tiles (you will have more of everything than you need except the center white tiles, so you can do some selecting for best fit, condition, and matching colors).
To attach the second end cap, start with a screw that is too long (e.g., 3/4 inch), screw it all the way in until it jams, and test how loose the puzzle fit is. Then repeatedly trim the screw a bit shorter and try again until the fit is just right. That is, because the rod is slightly shorter than the end to end distance, the fit is not determined by the length of the rod (another way to do this), but rather by how much the screw head / washer is protruding from the end of the rod when it is screwed in as far as it will go. The screws should jam in very tight so they will never move (but can still be removed in the future); can also add glue.
Finally place stickers on each end; you can glue them or use double sided tape.
Made by J. A. Storer, 2007.
(plastic, 1.5" square, 2.6" long)
Custom made by removing the center portion of a standard Missing Link puzzle. This makes a puzzle equivalent to the (much easier) 2-Section Whip-It Tower.
Here are what the other two sides and other end look like:
This is a fun to puzzle to make from left over parts from the construction of a puzzle such as the Doubled Missing Link, and could be made by using a new central spindle.
This particular puzzle made use of a version of the missing like puzzle in which the central spindle, rather than being solid and bumpy as is most common, is a smooth tube. The construction was very simple: Remove one sticker and end cap, take the puzzle apart, cut the spindle to just the right length, slide two sections onto the spindle with tiles placed appropriately, and screw the end cap back on with a 1" 6-32 screw. The screw has a loose fit in the tube but stays in place because it goes in an inch (and you can add glue if needed). The screw head and washer sit inside the recessed hole of the end cap, and the sticker is put back on to cover it up.
(a.k.a. Equator Ball, IQ Ball)
Hungarian Globe and Equator Ball, made circa 1982.
(metal covered plastic, 3 inches)
IQ Ball, circa 2000.
(plastic, 3 inches)
Three rings of 12 squares each (going around each of the three dimensions) can be rotated. The goal is to mix up the puzzle and then restore the original pattern, or in the case of the IQ Ball, the directions that were sold with it give different challenges. A number of 1980's and 1990's patents describe mechanisms for this puzzle, including the patent of R. Destics which describes a generalized mechanism (used by the Mozaika Puzzle) that can also twist along the equator, and the Magic Sphere puzzle allows faces to rotate. Jaap's Page presents a solution.
Further Reading
Jaap's Page, from: http://www.jaapsch.net/puzzles/equator.htm
Molnar GB Patent, from: www.epo.org - patent no. GB2088728
Green Patent, from: www.uspto.gov - patent no. 4,452,454
Green Second Patent, from: www.uspto.gov - patent no. 5,074,562
Liu Patent, from: www.uspto.gov - patent no. 5,114,148
Destics Patent, from: www.uspto.gov - patent no. 5,566,941
Maxim Patent, from: www.uspto.gov - patent no. 6,186,504
Patented by T. D. Chen 1998, copyright DaMert Co. 2005.
(plastic, 2.75 inches)
A generalization of the Hungarian Globe puzzle where six colored circular areas on the surface (red, orange, green, light green, blue, and purple) can rotate. This puzzle is all plastic with no stickers and works quite smoothly.
Further Reading
Chen Patent, from: www.uspto.gov - patent no. 5,816,571
K&T Toys,Inc., purchased 2007.
(plastic, 3.5 inches diameter by 6.5 inches long)
This is the "Limited Edition Patriotic Version"; this puzzle was also made with brown body. The directions give three increasingly hard challenges:1. Move the football from one side to the other.This puzzle can be solved in a fashion similar to the Fifteen puzzle (and a similar parity argument applies).
2. After mixing up the puzzle (e.g., after completing Challenge 1), return all the players to their respective sides (the end caps specify the red and blue sides of the puzzle).
3. Put the players into their correct sequentially numbered positions.
a.k.a. Wooden Screwball, Clever Toys Natural
Made by Clever Toys, 2008.
(wood, 3.5 inches diameter by 2.9 inches high)
This is a simpler version of the Rainbow Puzzle described on Jaap's Page, where the loops have only eight balls instead of ten (and the center ring moves only one row of balls) and when solved all balls in a loop have the same color.
Solution: Using two adjacent circles as scratch, it is easy to solve the other two. So without loss of generality assume that the puzzle is now solved except that in two adjacent circles, the red and black balls are mixed up. Rotate a black ball in the red circle to the center section, rotate the red ball in the black circle to one position away from the center section, spin the middle one position, rotate the black circle one unit, and spin the center section back. Keep repeating this step until solved. Note that this solution allows one to put the circles in any order.
Further Reading
Jaap's Page, from: http://www.jaapsch.net/puzzles/rainbowp.htm
a.k.a. Kaos
Patented by C. Hausammann 1993.
(plastic, 7 inches)
The top and bottom halves of these tubes can be rotated with respect to each other, and the balls can be shifted back and forth. Jaap's Page gives a solution. This puzzle was made in a number of versions that are the same except for the color of the balls and the packaging.
Further Reading
Jaap's Page, from: http://www.jaapsch.net/puzzles/chaos.htm
Hausammann Patent, from: www.uspto.gov - patent no. 5,176,382
Circa 1980's?
(plastic, 3.5 inches high by 2.75 inches diameter)
The top and bottom halves of the puzzle each have three tubes that can hold three balls each. By rotating the top and bottom halves with respect to each other, balls can be moved around to get to the solved state that has one empty tube and five tubes each containing three balls of the same color. This puzzle is in a similar theme to the Atomic Chaos puzzle, but easier to solve.
a.k.a. Stupid Cylinder
Czech Republic, circa 1990?
(plastic, 1.7 inches diameter by 2.7 inches long)
There are four columns such that when the puzzle is solved, each contains four tiles of the same color (red, green, blue, or yellow). The body can slide up and down and be used to rotate a row (which also rotates some blank tiles that are the same color as the body). The columns are not evenly spaced (two are adjacent and the other two are spaced apart from those and each other); below are some views of a solved puzzle. Jaap's Page gives a solution.
Further Reading
Jaap's Page, from: http://www.jaapsch.net/puzzles/pakovalec.htm
a.k.a. Billion Barrel, Tumbler Puzzle
Patented G. Yokoi 1983, made by Nitendo.
(plastic, 3.4 inches high by 2.8 inches diameter;
left 1980, green, blue, red, orange, yellow with black balls on green, yellow, red;
right 2009, orange, yellow green, blue, red with black balls on orange, red, green;
the Yoki patent also describes the Trillion puzzle) )
There are 23 balls in 5 columns, 4 of each of red, orange, yellow, green, blue, where three of the columns have an extra black ball. There are 6 rows of plastic rings around the puzzle where rows 1 and 6 cannot rotate, rows 2 and 3 rotate together, and rows 4 and 5 rotate together. The black body that holds the balls can slide up or down 1 unit inside the rings to shift the three longer columns. The goal is to put each of the 5 colors in their own column, with the three black balls on top of the three longer columns. Jaap's Page presents a solution. Here is a view of the other side of the solved puzzle, and a view of it mixed up:
Further Reading
Jaap's Page, from: http://www.jaapsch.net/puzzles/nintendo.htm
Martin's Page, from: http://www.smartbytes.co.uk/Tumbler/tumbler0.htm
Spanish Page, from: http://chelis.iespana.es/soto1.htm
Yokoi Patent, from: www.uspto.gov - patent no. 4,376,537
a.k.a. Russian Flower, Russian UFO, Soviet UFO
Made in the Soviet Union circa 1980's?
(plastic, 1.6 inch diameter disc, 2 inches across, 1.1 inches thick)
Three colors of balls must be arranged so that a single color shows on each side of the puzzle (and the third color is hidden). This puzzle was also made with green and orange bodies.
a.k.a. Loophole
Patented by F. Lammertink 1992, copyright 1991 Binary Arts.
(plastic, 6 inches diameter by 1.25 inches thick)
Two discs that can rotate with respect to each other hold a total of 35 balls in six three ball slots on each side, at any time one slot is missing one ball, creating a gap into which a ball from that slot can be rolled or a ball from the other side can be pushed through if the discs are rotated appropriately. The slots on each side are arranged as three spokes and three outer slots; the three colors of the balls in the spokes are the same as the three colors of the outer slots on the opposite side. Jaap's Page observes that this puzzle is relatively easy to solve by first solving the inner two balls of each spoke and then the remaining balls, essentially correcting one ball at a time.
Further Reading
Jaap's Page, from: http://www.jaapsch.net/puzzles/backspin.htm
Lammertink Patent, from: www.uspto.gov - patent no. 5,172,912
Circa 1990's?
(plastic, 2.6 inches by 4.75 inches, left Pepsi graphics, right dinosaur graphics)
Plastic pieces slide on a diagonal grid in a generalization of the Fifteen puzzle. Here are views of the other sides:
Circa 1990's?
(plastic, 2.6 inches by 4.75 inches, left Coke graphics, right Sprite graphics)
Pieces can slide up and down and rows can rotate; a generalization of the Fifteen puzzle. Here are views of the other sides:
Copyright Winning Moves 2006, sold by Rubiks.com.
(plastic, 2.6 inches)
Twist the ring and pull to remove that triangle. Then slide the other triangles around to make different patterns. It is shipped in the pattern shown above with red on top, green on the bottom and a band of alternating blue and yellow around the middle.
a.k.a. Orb-It, l'ORBS
Patented by C. Wiggs and C. Taylor 1985, made by Parker Brothers.
(plastic, 3.5 inches)
When solved, the north pole ring has 8 yellow, the upper equator 20 green, the lower equator 20 red, and the south pole 8 blue beads. The puzzle can twist in 45 degree increments. The 45 (also -45, 135, and -135) degree rotations give one continuous loop along which all beads can rotate; fun, but the beads are hard to move this way, and it is not needed to solve the puzzle. A 90 (and -90) degree rotation creates two cycles of 28 beads that connect halves of the pole and equator rings. The 180 degree rotation joins opposite halves of the pole and equator rings.Based on the observation that incorrect beads always occur in multiples of 2, a simple solution, which is presented on Jaap's Page, works in three steps:
1. Use 90 deg. twists to get yellow/blue to poles, green/red to equator.Steps 2 and 3 are easy; place one incorrect bead in each ring on opposite sides of the twist line, and then twist, rotate, twist, and repeat as needed. For step 1, a 90 degree twist followed by a rotation by one bead moves two beads from the poles to the equator and ice-versa. So first select an incorrect bead on each ring; if there are incorrect beads on only one pole or one equator ring, first use the ideas of Steps 2 and 3 to get at least one incorrect bead on each ring. Next, place the north pole incorrect bead next to the line on the left hemisphere, the upper equator incorrect bead next to the line on the right hemisphere, the lower equator incorrect bead next to the line in the rear on the right hemisphere, and the south pole incorrect bead next to the line in the rear on the left hemisphere. Then twist 90 degrees, rotate the vertical cycle counter clockwise one bead, and twist back. Repeat as needed.
2. Use 180 deg. twists to get north yellow, south blue.
3. Use 180 deg. twists to get upper equator green, lower equator red.
Further reading:
Jaap's Page, from: http://www.jaapsch.net/puzzles/orb.htm
Wiggs Patent, from: www.uspto.gov - patent no. 4,553,754
Left Toy Brokers Ltd. / www.rubiks.com circa 2000, right Chinese purchased 2007.
(material, 4.5 inches)
Four loops of eight balls each are arranged in two perpendicular intersecting pairs. Since four of the balls are located at the intersections of the loops, there are a total of 28 balls, seven of each of the four colors (so when solved, each loop has one intersecting ball of its color and one intersecting ball of the other color). Each of the two axles has a button which when pushed in locks the two loops on that axle so that they must rotate together, which gives the puzzle three levels of difficulty (neither pushed, one pushed, or two pushed). Unfortunately, once a button is pushed, that cannot be undone so that someone else can enjoy the easier level (so if you like this puzzle, you may want to get three of them, and leave them set to each of the three levels). The goal is to mix up the puzzle and then put the colors back to the 4 loops. Jaap's Page presents a solution (for all three button states, and which works independent of what state the puzzle was in when a button was pushed), and the puzzle was sold with a solution booklet. Here are photos of the other sides:
Further Reading
Jaap's Page, from: http://www.jaapsch.net/puzzles/rubshll.htm
Solution booklet from Rubiks.com:, from: http://www.rubiks.com/World/Rubiks%20downloads.aspx
Patented by John Haris 1997.
(plastic, 3.5 inches)
This puzzle combines manipulation of the body (changing its shape) with movement of balls. The Harris patent includes figures showing its manipulation and construction. Jaap's Page presents a solution.
Further Reading
Jaap's Page, from: http://www.jaapsch.net/puzzles/astrolab.htm
Powerstrike Page, from: http://www.powerstrike.net/puzzles/solutions/astrolabacus.htm
Harris Patent, from: www.uspto.gov - patent no. 5,645,278
a.k.a. Bloxbox, Qrazy Qube
Basic idea dates back to 1889.
(clear plastic box containing 7 red cubes with blue and white dots, 1.5 inches)
A box with 7 cubes and an empty space that allows you to move cubes around by tilting. One must shuffle the cubes so as to have only blue dots touching the faces of the box and three white dots showing in the position with the empty space. There is a little hole in one corner that had a pin inserted into it to prevent the puzzle from being disturbed during shipping. The puzzle is pleasant to use, and doesn't require great dexterity to move cubes. This basic idea is presented in the 1889 Rice patent, and also in the patents of Sinden and Postasy, and the design of this puzzle has been credited to Piet Hein 1972. Jaap's Page presents a solution.
Here are some other versions (the rightmost is a Soviet version). A parity argument implies that not all positions are reachable from a given position, and you cannot exchange two cubes without changing the configuration of the others. So if you try to solve a puzzle of this type and end up with two cubes exchanged, then it must be the other color has to be on the outside.
Further reading:
White with
red/blue dots.
(1.5 inches)
Blue with
red/white dots.
(1.5 inches)
Black with
red/white dots.
(1.5 inches)
Black with
orange/white dots.
(1.5 inches)
White with
red squares.
(1.4 inches)
Jaap's Page, from: http://www.jaapsch.net/puzzles/varikon2.htm
Rice Patent, from: www.uspto.gov - patent no. 416,344
Sinden Patent, from: www.uspto.gov - patent no. 3,841,638
Postasy DE Patent, from: www.epo.org - patent no. DE3027556
Patented by D. Kosarek 1974; 2x2x2 version dates back to 1889.
(clear plastic box containing red cubes with blue and white dots, 2.1 inches)
The center cube and the six cubes that are the center of each of the 6 faces form a single central solid "cross", leaving only 19 cubes that can move around this central cross by tilting the box. Like the Varikon Box 2x2x2, one must shuffle the cubes so as to have only blue dots touching the faces of the box and three white dots showing in the position with the empty space; the puzzle is pleasant to use (and doesn't require great dexterity to move cubes). There is a little hole in one corner that had a pin inserted into it to prevent the puzzle from being disturbed during shipping.
Jaap's Page presents a solution (using a Rubik's cube type notation) that solves the bottom two layers and then solves the top layer by repeatedly exchanging cubes as needed.
This is the same puzzle as Inversion, Inversion, and similar to the Vadasz Cage 3x3x3, a smaller version of Peter's Black Hole, and Mad Marbles. Here are some other versions:
White with red/blue dots.
(2.1 inches)
White with red/green dots.
(2.1 inches)
White with red/green dots.
(2.1 inches)
Further reading:
Jaap's Page, from: http://www.jaapsch.net/puzzles/varikon3.htm
Rice Patent, from: www.uspto.gov - patent no. 416,344
Coe Patent, from: www.uspto.gov - patent no. 785,665
Sinden Patent, from: www.uspto.gov - patent no. 3,841,638
Kosarek Patent, from: www.uspto.gov - patent no. 3,845,959
Postasy DE Patent, from: www.epo.org - patent no. DE3027556
Patented by P. A. Roberts, 1985.
(plastic, 2.6 inches)
Like the older Varikon Box 3x3x3, but here the 19 cubes are held in place by the edges of the central cross, and you use the puzzle by simply pushing the cubes around. Each cube is colored blue on three sides adjacent to one corner and red on three sides adjacent to the opposite corner. The puzzle is to go between all red and all blue on the outside. Here is what the box says:
Further reading:
Jaap's Page, from: http://www.jaapsch.net/puzzles/varikon3.htm
Roberts Patent, from: www.uspto.gov - patent no. 4,511,144
a.k.a. Inside Out, Magic Jack, IQ Cube
Peter's Black Hole, circa 1990's.
(plastic, 3.25 inches)
One can reach in with a finger to move cubes inside a cage. The design of the Vadasz cage is often credited to Jozsef Vadasz circa 1995, although this basic idea is described in a number of patents dating back to the early 1900's; the patent of Peter Kassan shows a slightly more complex mechanism with a central cage. These puzzles can be viewed as generalizations of the Fifteen puzzle to three dimensions. It is most fun to use them in a more limited way where you just push from the ends (the only way needed for the 2x2x2 version), but the cubes can be moved individually (and you have to assume that this may have been done when you pick it up after someone else has used it). Jaap's Page gives analysis and a solution.
Vadasz Cage 2x2x2,
Hungary circa 1990's.
(plastic, 2.1 inches)
Vadasz Cage 3x3x3,
Hungary circa 1990's.
(plastic, 3 inches)
Vadasz Cage 4x4x4,
Hungary circa 1990's.
(plastic, 3.75 inches)
Further Reading
Jaap's Page, from: http://www.jaapsch.net/puzzles/blackhole.htm
Coe Patent, from: www.uspto.gov - patent no. 785,665
Wooster Patent, from: www.uspto.gov - patent no. 1,518,889
Kosarek Patent, from: www.uspto.gov - patent no. 3,845,959
Kassan Patent, from: www.uspto.gov - patent no. 4,432,548
Circa 1980's?
(plastic, 1.8 inches square by 2 inches high)
This puzzle is similar to (but not the same as) the 3x3x3 Varikon Box, where balls are moved by tilting the box. The colored balls surround a 1 by 1 by 3 unit high core, so that when solved, there are 8 green balls in the bottom layer, 8 blue balls in the center layer, and 7 red balls in the top layer.
Designed and made by J. A. Storer, 2007.
(glued 2 inch plastic golf ball display box containing seven 22mm dice)
These two puzzles work like a 2x2x2 Varikon Box (where cubes are moved by tilting the box), but are easier to solve. Both are shown above in a random state, and for both the goals is:Pick a number and arrange so that number cannot be seen from any side.The black box has a solution for any of the numbers 1, 2, 3, 4, 5, or 6.
The white box can only be solved for 1 or 6 (for each of the numbers 2, 3, 4, and 5, there are four cubes that have this number facing in the same direction)
Patented by W. Clark 1984, made by Innoventures Inc.
(plastic, 1.8 inches)
Like the 2x2x2 Varikon Box 2x2x2 Varikon Box except that through holes in the box a finger can rotate a cube. Jaap's Page observes that it can be solved by first rotating each cube to its correct orientation and then solving like the 2x2x2 Varikon box. Here are the directions on the back of the package:
Further Reading
Jaap's Page, from: http://www.jaapsch.net/puzzles/clark.htm
Clark Frist 1984 Patent, from: www.uspto.gov - patent no. 4,424,971
Clark Second 1984 Patent, from: www.uspto.gov - patent no. 4,488,725
a.k.a. Pionir Cube
Made by Artex, Hungary, 1984.
(plastic, 2 inches)
A total of 67 balls can be moved along tracks one the inside edges of the box by tilting the box (e.g., in a fashion similar to the Varikon 3x3x3 Box); Varikon 3x3x3 Box); there are 7 balls on each edge (with the corner balls being shared between three edges), where one ball is missing. Each side of the box has a paper label with four colored dots on it. All the balls are black, except for 4 red, 4 green, and 4 yellow balls, which in the solved position, must be located in the middle of edges next to the same colored dot on the labels. Jaap's Page presents a solution.
Further Reading
Jaap's Page, from: http://www.jaapsch.net/puzzles/pionir.htm
Matchbox 1990.
(plastic with internal parts and magnets, 2.7 inches)
Plates inside a hollow cube that have white and red dots on them can be manipulated by tilting the cube; the goal is to make only white dote shown in the holes that have the pattern of a standard die. The 1993 patent of J. Bognar and E. Rubik of a similar mechanism with plated with a single hole on each side into which a finger can be pushed. Jaap's Page describes the configuration of the plates and gives a solution. Here is the English portion of the directions from the back of the box:
Further Reading
Jaap's Page, from: http://www.jaapsch.net/puzzles/rubdice.htm
McFarren's Page, from: http://www.geocities.com/abcmcfarren/math/r90/dicenot.htm
Koller's Page, from: http://www.mathematische-basteleien.de/dice.htm
Bognar-Rubik Patent, from: www.uspto.gov - patent no. 5,184,822
a.k.a. Pyramid Piling Puzzle, Brahma Puzzle
Very old design, this puzzle purchased from Bits And Pieces 2007.
(wood stand and seven wood discs, 2.3" by 5.3" base by 3.5" high)
On Post A there are n rings of different sizes, in the order of the largest ring on the bottom to the smallest one on top. Posts B and C are empty. The object is to move the n rings from Post A to Post B by successively moving a ring from one post to another post that is empty or has a larger diameter ring on top.
Solution: Since any of the rings 1 through n-1 can be placed on top of ring n, all n rings can be moved by invoking the recursive procedure TOWER:procedure TOWER(n,x,y,z)TOWER(n,x,y,z) makes 2n-1 moves; e.g, TOWER(3,A,B,C) takes 7 steps:if n>0 then beginTOWER(n-1,x,z,y)end
write "Move ring n from x to y."
TOWER(n-1,z,y,x)
end
"Unwinding" the recursion of TOWER, yields the following simple iterative algorithm that moves the discs on post in the clockwise direction:if n is odd then d := clockwise else d := counterclockwise
repeatMove the smallest ring one post in direction d.
Make the only legal move that does not involve the smallest ring.
until all rings are on the same post
Pyramid Piling Puzzle, Well-Maid Wood Products, Suffield, CT, unknown age.
(cardboard box 3.7" x 5" x 3/4", wood base and pieces, directions, infor. sheet;
the discs were lost at some point and replaced)
Further Reading
Excerpt from J. A. Storer's book.
Wikipedia Page, from: http://en.wikipedia.org/wiki/Towers_of_hanoi
Wolfram Mathworld Page, from: http://mathworld.wolfram.com/TowerofHanoi.html
Claus Page, from: http://www.cs.wm.edu/~pkstoc/toh.html
Ajtai Patent, from: www.uspto.gov - patent no. 5,992,851
a.k.a. a.k.a. Cardan's Rings, Baguenaudier
Very old design, this one owned by J. A. Storer's grandfather, circa 1900?
(2.4 by 8.5 by 1.75 inches high wood box with key and 6.5 inch long puzzle)
Each ring is attached to a post and, except for the rightmost ring (the one farthest from the handle), each goes around the post to its right (and under the ring to its right). Rings that are not on the skewer can pass sideways through the skewer. Initially, the skewer goes through all the rings. The goal is to remove the skewer from the rings (and then put it back).
Solution: Observe that the only two ways to move a ring are to put the rightmost ring on or off the skewer, or, a ring can be put on or off the skewer if and only if the ring to the immediate right is on but all other rings to the right are off. This leads to a simple iterative solution in a similar spirit to the Towers Of Hanoi puzzle; we use the phrase "complement a ring" to mean take it off if it is on or put it on if it is off:Take the rings off:Start with all rings ON.Put the rings on:
repeatMake the only legal move that is not complementing the rightmost ring.
Complement the rightmost ring.
until all rings are OFFStart with all rings OFF.
repeatComplement the rightmost ring.
Make the only legal move that is not complementing the rightmost ring.
until all rings are ON
Gray codes of n bits are a binary counting system where only one bit changes from the representation for an integer i to the representation of i+1, 0 &le i &le 2 n - 1. Let B(i,n) denote the standard binary representation of i using n bits, G(i,n) the Gray code of n bits, XOR the exclusive or operation, and ShiftRight the operation of shifting the bits of a code one position to the right (discarding the rightmost bit and setting the leftmost bit to 0). Although Gray codes are not in general unique, a standard form is one where:G(i,n) = B(i,n) XOR ShiftRight(B(i,n))Here is the correspondence for n=4;
all 4 bit binary sequences are shown, but we only need entries 0 through 10:Observe that when going from one row to the next, every other time it is the rightmost bit that changes, and for the other times a bit changes where the bit to its right is 1 and all bits to the right of that are 0. Hence, if we let 0 denote a ring off and 1 denote a ring on, then one can see that the Gray code sequence corresponds to our solution for the Chinese rings; that is, for the case of 4 rings, taking them off corresponds to moving from row 10 to row 0 in the above table, and putting them on corresponds to moving from row 0 to row 10.
The number of moves to put the rings on or off is the same, so let's count the number of moves to take them off. We can express our iterative solution recursively as follows:Represent the rings as an array R[1] .. R[n] where R[1] corresponds to the leftmost ring, and R[i] is 0 if the corresponding ring is off and 1 if it is on. Let FLIP(i) denote complementing R[1] through R[i], then set all positions to 1 and call FLIP(n):The number of moves M(n) for FLIP(n) is given by the recurrence relation:
procedure FLIP(i)
if i=1 then Complement R[1].
else if i=2 then Complement R[1] and R[2].
else doFLIP(i-2)
Complement R[i].
FLIP(i-2)
FLIP(i-1)
endM(n) = M(n-1) + 2M(n-2) + 1Two simple proofs by induction, one for when n is even and one for when n is odd, can now be used to show that the solution is:(2n+1-2)/3 if n if n is evenThe first few values of M(n) are:
(2n+1-1)/3 if n if n is odd1, 2, 5, 10, 21, 42, 85, 170, 341, 682. ...For the puzzle pictured here, which has seven rings, the solution is 85 moves.
Note: Sometimes people count the moving of the two rightmost rings as one move, in which case it can be shown that the number of moves is reduced to:2n-1-1 if n is evenAnd now the first few solution values become:
2n-1 if n is odd1, 1, 4, 7, 16, 31, 64, 127, 256, 511, ...
Wikipedia Baguenaudier History Page, from: http://en.wikipedia.org/wiki/Baguenaudier
Jaap's Page, from: http://www.jaapsch.net/puzzles/spinout.htm
IES Page, from: http://www.daviddarling.info/encyclopedia/C/Chinese_rings.html
Jim Loy's Page, from: http://www.jimloy.com/puzz/chinese.htm
JCKLueng Page, from: http://staff.ccss.edu.hk/jckleung/ninering/solu_eng.html
Jill Britton's Page, from: http://britton.disted.camosun.bc.ca/patience/patience.htm
Devil's Halo Page, from: http://www.puzzlemuseum.com/month/picm05/200501d-halo.htm
Wikipedia Gray Codes Page, from: http://en.wikipedia.org/wiki/Gray_code
Answers.com Gray Codes Page, from: http://www.answers.com/topic/gray-code?cat=technology
Wolfram Mathworld Gray Codes Page, from: http://mathworld.wolfram.com/GrayCode.html
Joyner and McShea Gray Codes Page, from: http://eng.usna.navy.mil/~wdj/gray.htm
Conrad's Gray Codes Page, from: http://www.yagni.com/graycode
Everything Gray Codes Page, from: http://everything2.com/node/114662
PC In Control Gray Codes Page, from: http://www.pc-control.co.uk/gray_code.htm
Kamruzzaman Gray Codes Page, from: http://acm.uva.es/p/v104/10455.html
Doran Gray Codes Page, from: http://members.tripod.com/~rvk/index-2.html
Whealton Gray Codes Page, from: http://www.washingtonart.net/whealton/gray.html
Sluss Patent, from: www.uspto.gov - patent no. 3,784,206
Guindon Patent, from: www.uspto.gov - patent no. 6,508,467
Patented by W. Keister 1972, made by Binary Arts / Think Fun.
(top: plastic, 12.25 inches;
bottom: plastic, nnn inches))
There is a bar with knobs on it in a track. There is only one position along the track where a knob can be turned. When all of the knobs are turned horizontal (curved end to the left in the photo above) the bar can slide all the way out. There are only two possible moves at each point, and so to solve, one can repeatedly choose the move that does not return the puzzle to the previous position. Start by turning the rightmost knob.
The original version is shown first above. Binary Arts, which became Think Fun, later made the one shown second above, which allows the knobs to be reset (by flipping down the end and sliding out the bar); this one was purchased in 2008.
Jaap's Page presents this puzzle, which is essentially the same puzzle as the Hexidecimal Puzzle (described in another Keister patent) and the Chinese Rings (see that page for information about Gray Codes and additional links).
Further Reading
Jaap's Page, from: http://www.jaapsch.net/puzzles/spinout.htm
Keister Patent, from: www.uspto.gov - patent no. 3,637,215
Patented by W. Keister 1972, made by Binary Arts.
(Cherry, 8.75 inches, in a 6.2 by 10.75 by 2.2 inch cardboard box)
There are eight bars that can either be up or down; and four fingers that can be either up (one) or down (zero). In the photo below, the leftmost two bars are up, the third bar from the left is down, the fourth and fifth bars from the left are up, the rightmost three bars are down, the left three fingers are up (three ones), and the rightmost finger is down (a zero). The assembly that holds the bars cannot slide out to the right and can only slide out to the left if all the bars are up. The finger assembly can be pushed in (it is spring loaded) to cause a center portion of the back edge to go back, allowing the bar that is lined up with the right edge of the finger assembly to move up or down; the difficulty is that the finger assembly can only push in when each 1-finger is aligned with a down bar and each 0-finger is aligned with a down bar (or the finger is to the left of the bars); in the photo below, it can be pushed in. The fingers can be set to any of the sixteen possible patterns by pulling out the peg that runs through them and rotating each as desired. The corresponding sixteen puzzles all have the goal of starting with all bars down, and sliding the finger assembly out to the left. Setting 1111 allows the bars to be moved up one at a tome and the bar assembly easily slid out. Setting 1110 is the hardest setting, which gives a puzzle equivalent to the Chinese Rings, and requires 170 moves.
The setting of 1110 that requires the longest sequence of moves can be solved exactly like Spinout (described in another Keister patent) or the Chinese Rings puzzle (see that page for information about Gray Codes and additional links), where moves alternate between the rightmost bar and the only other legal move. Shorter solutions for the other patterns can be solved by along the lines of the hints card provided with the puzzle. Jaap's Page gives some history of this puzzle (it was the first puzzle made by Binary Arts, which became Think Fun), cites an article about the inventor, and presents minimal solutions for each level, as well as some additional analysis of the solution space diameter (the maximum number of moves to go between any two positions, not necessarily the start and end positions); here is a table of the minimal solution lengths:
Further Reading
Jaap's Page, from: http://www.jaapsch.net/puzzles/hexadec.htm
Keister Article, from: http://www.puzzles.com/products/ElephantSpinOut/ElephantInventor.htm
Keister Patent, from: www.uspto.gov - patent no. 3,637,216
Designed by Vilmos Serestey and sold at the Atlanta 1996 Olympics.
(plastic, 25 rings + base, 7 inches wide by 3.5 inches tall)
Five rings of each color numbered, 1 through 5. The only two legal moves are to move 2 rings at a time or to move 3 rings at a time. The posts are only long enough to hold 7 rings. After mixing up the rings, get them back to the solved puzzle where rings of each color on their correct base, arranged in order from 1 on the bottom to 5 on top. An easier puzzle is to ignore the numbers. Another puzzle is get five colors on each post (in the same order).
A Solution: Assume we start with 5 rings on each post (if not, it is always easy to make it so). The following sequence temporarily "parks" the top ring of one post (call it A) on another post (peg B):
- PARK: Move 2 rings from B to A, then move 3 rings from A to B.
(You can also "double park" by repeating this operation twice.)
- UNPARK: Move 3 rings B to A, then move 2 rings from A to B.
(If double parked, repeat this twice, or if another post C currently has only 5 rings, you can put back the two rings in reverse order by moving 2 rings from B to C, 2 rings from B to A, and 2 rings from C to B.)
Using this idea, we can do the following two key transformations:
- The top rings of any two posts can be exchanged.
(In fact with double parking you can exchange the top two rings).
- The rings of a given post can be permuted in any order. (The top 4 can each be parked on the other four posts so that they can be put back in any order. If the bottom ring also needs to be moved, it can be double parked with one of the rings that is going to one of the top 4 positions.)
The ability to permute the rings of a post combined with the ability to exchange the top rings of any two post suffices to solve the puzzle. Of course, additional shortcuts can be devised.
Designed by Toshio Akanuma, originally made by TRICKS Co. Tokyo Japan, 1983;
this one made by J. A. Storer, 2009.
(Ebony, Walnut, Purple Heart, Apple, brass, 2" x 8" x 3.75")
In the theme of the Towers Of Hanoi puzzle, but with a more complex analysis. Exchange the 4 tiles on levels 1, 2, 3, 4 on the left (marked with brass screws) with the 4 tiles on the corresponding levels on the right; tiles must be moved by sliding off one post and on to another, where the posts are long enough to hold a tile at level 5. The puzzle is constructed so that no tile can move below its initial level.
The original version made in 1983 has 10 identical tiles on each side that move in a board, where tracks on the back of the tiles enforce the condition that no tile can move lower than its first position. Baxter's Page has references to an analysis of the general solution for a puzzle of n tiles on each side (see also Jaap's Page), and Baxter's paper gives the following table of the number of moves required for puzzles of size 1 through 10 (where the entry for 10 is an upper bound and the others have been verified by computer to be optimal).
Further Reading
Baxter's Page, from: http://baxterweb.com/puzzles/panex
Baxter's paper, from: http://baxterweb.com/puzzles/panex/panex2rev.pdf
Jaap's Page, from: http://www.jaapsch.net/puzzles/panex.htm
Manasse and Sleator paper, from: http://baxterweb.com/puzzles/panex/panex-v1d.pdf
Manasse, Sleator, Wei, Baxter paper, from: http://baxterweb.com/puzzles/panex/panex5.pdf
Panex Search Program, from: http://baxterweb.com/puzzles/panex/program.htm
Bagley Play Panex Page, from: http://gwyn.tux.org/~bagleyd/java/PanexApp.html
Henderson Play Panex Page (4 high), from: http://www.cheesygames.com/panex
Patented by D. Rom 2004, made by elogIQ.
(plastic, left 5 inches with 1" balls, right 3.5 inches with 1" balls)
Comes in the standard 3 x 3 version (which was also made in a clear body) and the mini 2x2 version. Rotating a ball up or down makes all balls in the same column rotate the same way, and rotating a ball left or right makes all balls in the same row rotate the same way. Each ball has six colors.; the goal is to mix up the puzzle and then restore it to each side having a single color facing up. The puzzles come with solution hints, and Jaap's Page presents a solution. Here are what the reverse sides of the two puzzles look like:
Further Reading
Jaap's Page, from: http://www.jaapsch.net/puzzles/cmetrick.htm
Rom Patent Application, from: www.uspto.gov - application no. 2004/0000756
Patented by D. Rom 2004, made by elogIQ.
(plastic, 3.5 inches with 1.5 inch diameter balls)
Each of the six balls can rotate in each of the three directions. Each pair of adjacent balls shares a disc (so there are a total of 20 discs), and rotating a ball causes the shared disc or discs to move and be replaced. When solved, each ball shows a single color (red, blue, green, or yellow) and the hidden discs are all white.
A harder version of the puzzle, called Cmetrick Too Hard (two views shown below), has dots in the middle of the discs that must be the same color on each side of the puzzle when solved.
The puzzles come with solution hints, and Jaap's Page presents a solution.
Further Reading
Jaap's Page, from: http://www.jaapsch.net/puzzles/cmetrick.htm
Jaap's Contest Page, from: http://www.jaapsch.net/puzzles/cmetrick2c.htm
Rom Patent, from: www.uspto.gov - patent no. 6,773,011
Designed by Oskar van Deventer, made by Recent Toys International; the box this one came in says copyright DaMert Co. 2005.
(plastic, each edge is 3.5 inches)
Four balls each have a number of circular depressions that allow them to be packed tightly together inside a pyramid shaped cage. A ball can rotate only if it sits in the depressions of at least two other balls. The goal is to rotate the balls so that each side is a single color (red, green, blue, or yellow). Here are the other two sides:
By observing that the green and blue faces have only one depression, Jaap's Page observes that a relatively simple solution proceeds by solving green and blue first (to allow more depressions available for the remainder of the solution). That is, position the red-green-blue corner, then the green-blue-yellow corner, then the third planet on the blue side, and finally the remaining planet, where the last step may require some temporary rotations of the other balls.
Further Reading
Jaap's Page, from: http://www.jaapsch.net/puzzles/planets.htm
Patented by L. A. M. J. DeBergh 1996, made by LD Games, Belgium.
(plastic, 4.5 inches by 7/8 inch thick;
one the bar it says "SATURN 2x4 colors",
and on the other side of the bar is says "LD Games Belgium Patented C 1994")
Each side of the ring has 16 discs, where each of the 64 disc sides are colored with one of 14 colors. The goal is to have exactly 4 colors showing on each side (arranged in 4 sets of 4) for a total of 8 visible colors, where the remaining 6 colors are hidden. This puzzles is really a pencil and paper problem of determining which of the 14 colors are the 8 visible colors (see the next page); for the white body puzzle above they are:Visible: yellow, pink, magenta, purple, light green, green, blue, grayOnce the 8 visible colors have been determined, solving the puzzle is very easy. The bar across the center in the photos above, which the directions refer to as the "switch", is in the solved position that prevents the puzzle from being mixed up. Rotating the switch along its axis 90 degrees exposes a track on both sides. The first two positions on each side can each be used to temporarily park one or two discs, and the third position on the track allows a disc to pass from one side of the track to the other. Rotating the switch 180 degrees allows one to exchange discs from top to bottom or flip a disc:
Hidden: white, orange, red, light blue, brown, black
(Black body is the same except that brown visible and gray hidden.)
To solve:
- Flip all discs that have a hidden color showing.
- If a color is showing on 5 discs (all colors are on at most 5 sides), find the disc that does not have a hidden color on the reverse side and flip that one.
- Exchange discs one or two at a time until only four colors show on each side.
- Rearrange colors on each side into any desired pattern (e.g., 4 groups of 4).
Flip each disc to make a list of 32 color pairs that are comprised by the discs (see the next page). The number of times each color occurs is:
We refer to the colors that appear only 4 times as the sparse colors. The puzzle is not so simple as the 6 sparse colors are the 6 hidden colors.
A key observation is that If a sparse color is hidden, then all colors that appear on the opposite side of a disc with that sparse color must be visible. To determine which are the visible colors, we can employ some simple deductions. We do this for the white body puzzle; the logic for the black body puzzle is similar with brown and gray reversed:Jaap's Page gives a similar solution (that motivated this one).
- There are two discs that have a sparse color on both sides, (brown, gray) and (brown, pink). It turns out that brown is hidden and gray and pink are visible (if we had guessed incorrectly and chosen brown as visible, then in the following steps one quickly reaches a contradiction where there is a color that can be neither visible or hidden).
- Brown is also paired with green and yellow, so at this point we know that 4 of the visible colors are gray, pink, green, and yellow.
- By checking our list of 64 pairs, we see that blue is paired with 4 additional colors (red, black, light blue, and white) and so if blue was hidden, that would add 4 more visible colors, making a complete set of eight. But this cannot be possible, because now light green, for example, cannot be visible (because that would make 9 visible colors) and cannot be hidden (because light green is paired with orange which is not one of these 8). Hence blue must be the 5th visible color.
- Similar to step 3, light green must be the 6th visible color.
- Similar to steps 3 and 4, magenta must be the 7th visible color.
- Similar to steps 3, 4, and 5, purple must be the 8th visible color.
Here is a tabulation, listed in alphabetical order, of the disc colors that appear in the two puzzles show in the photos on the first page. Although both have the same numbers of each color, the pairings are not the same:
Further Reading
Jaap's Page, from: http://www.jaapsch.net/puzzles/saturnld.htmm
DeBergh WO Patent, from: http://www.wipo.int - patent no. 0,000,000
Patented by S-H Juang, 1988.
(plastic, 2.8 by 11/16 inches)
Each of the 12 windows is positioned over a little drum that can be rotated to show one of the four patterns red square, green circle, blue triangle, or yellow squiggle. Three of the windows are marked with four dots on the outer edge (in the photo above, going clockwise from the top, the marked windows are at positions 2, 5, and 9). Rotating the front face clockwise one position causes the drums in each of the three marked windows to cycle by one pattern. Rotating the front face count-clockwise repositions the windows without rotating any drums.
For example, if R denotes a clockwise rotation and C a counter-clockwise rotation, then repeating the two moves RC four times cycles the drums of the three marked windows four times (causing each to show the other three patterns and return to the pattern in which it started), and leaves the state of the puzzle unchanged.
The goal is to make all the windows show the same color. Jaap's Page gives a solution that can be used to solve for any of the four colors.
Further Reading
Jaap's Page, from: http://www.jaapsch.net/puzzles/orbik.htm
Juang Patent, from: www.uspto.gov - patent no. 4,752,074
Tobar Co. Challenge Games 2006; also sold by Recent Toys Internatioal.
(plastic, 4.75 inches diameter by 1 inch thick)
Eight three dimensional cross pieces each have a tip facing the top, a tip facing the bottom, two tips facing horizontally, and two tips facing vertically. A move consists of flipping a cross towards the empty position. For example, in the photo above, the cross in the center of the top row can be flipped down to the middle, leaving the to horizontal ends the same, causing the top and bottom tips to face vertically, and causing the formally vertical tips to face the the top and bottom. The goal is to mix up the puzzle then restore it so that there is a single copor of tips facing the top and a single color facing the bottom. The solved puzzle shown above has red tips on top, and below is a photo of the other side that has blue tips. Jaap's Page presents a solution.
Further Reading
Jaap's Page, from: http://www.jaapsch.net/puzzles/crosstsr.htm
Copyright Matchbox 1988, patented by C. Wiggs and C. Taylor 1989.
(plastic, 4.25 inches diameter by 1 inch thick)
Nine clocks are on each side (the reverse side is shown on the right above) are arranged in a 3 by 3 array with a yellow button and a knob at each corner. Each of the four yellow buttons can be up or down. Turning each of the four knobs on the side of the clock spins some subset of the clocks that depends on the buttons (all turn clockwise or counter clockwise depending on the direction the knob is turned), according to the following rules:
Adjacent to a down button: Turns all corner clocks adjacent to a down button.
Adjacent to an up button: Turns all corner clocks adjacent to an up button and for each of these corner clocks, the three clocks closest to them also turn.
The goal is to mix up the puzzle and then restore both sides to have all hands pointing up. Jaap's Page presents a solution that essentially solves one side at a time as follows:
- Make all non-corners point the same way: Put the top two buttons up, the bottom two down, and turn a top knob until the center clock matches the bottom middle clock (note that the bottom middle does not move and only the corners on the reverse side move); repeat three more time on successive 90 degree rotations of the puzzle.
- Make all non-corners point up: Put all buttons up and rotate all non-corners to point up.
- Repeat step 1 on the reverse side.
- Synchronize the corners on the reverse side: Since the corners are always the same on both sides, this step will synchronize corners on both sides, but be sure to do this from the perspective of the reverse side. Put the top left button down, the other three buttons up, and turn the top right knob until the center clock matches the upper left clock (note that the upper left clock does not move and the others all move together); repeat three more time on successive 90 degree rotations of the puzzle.
- Repeat Step 2 on the reverse side.
Further Reading
Jaap's Page, from: http://www.jaapsch.net/puzzles/clock.htm
Safalra's Page, from: http://www.safalra.com/other/rubiks-clock-solution
Stefan Pochmann's Page, from: http://www.thedryeraseboard.com/mechpuz/rubiksclock/solution
Dry Erase Board Page, from: http://www.stefan-pochmann.de/spocc/speedsolving/clock
Christian Eggermont's Page, from: http://web.inter.nl.net/users/C.Eggermont/Puzzels/Clock.html
Wiggs Patent, from: www.uspto.gov - patent no. 4,869,506
Mag-Nif Inc., 1989.
(plastic, 4.1 inches by 1.75 inches high)
Six red buttons can be pushed into one of three vertical positions; when the correct combination of positions is achieved, the puzzle comes apart into three sections. Here are views of the bottom of the puzzle and the bottom of the box, which invites you to purchase a solution sheet:
Solution: Leave every other button at the top position and push the other three to the middle position (none of the put-ons are pushed to the bottom position). The sections can then slide apart by pushing two opposite places on the top in directions roughly 90 degrees to each other.
a.k.a. Mind Twister
Patented by Y-J. Husn, 1993.
(plastic, 3.25 inches)
Each of six rotating discs has slots to hold eight numbers. In the solved position, each disc has the numbers 1 to 8 of its color in clockwise numerical order, except the white disc which has the number 1 to 7 in clockwise numerical order and one empty slot. Where two discs are tangent and one of the discs has an empty slot at that position, the number of the other disc at that position can be slid into the empty slot. The object is to mix up the puzzle and then restore to the solved state. Jaap's Page presents a solution. Here is a photo of the other side of the puzzle:
Further Reading
Jaap's Page, from: http://www.jaapsch.net/puzzles/wisdom.htm
Hsun Patent, from: www.uspto.gov - patent no. 5,215,305
a.k.a. SpongeBob Cube
Burger King promotional item, 2004.
(plastic, 2.5 inches)
An easy but fun puzzle where the top and bottom halves can be rotated with respect to each other and a piece can be slid up and down. Jaap's Page observes that this puzzle is like a 2 high by 4 column Whipit Tower where all pieces are different (or similar to a small Babylon Tower), and presents a solution.
Further Reading
Jaap's Page, from: http://www.jaapsch.net/puzzles/spongebob.htm
Designed by Ferdinand Lammertink, copyright ThinkFun 2005.
(plastic, 3 inches by 6.25 inches with 1.5 inch diameter wheels)
Two tracks, each with five squares, can slide horizontally to three positions (left, center, and right). Each square has the same number on both sides, A pair of wheels on either side of the central 2 by 3 array of numbers can be used to flip them. The basic goal is to make the pattern 0 to 9 (i.e., 0 to 4 on the top row and 5 to nine on the bottom row). The directions also challenge you to make other patterns.
Further Reading
Jaap's Page, from: http://www.jaapsch.net/puzzles/flipside.htm
Passion For Puzzles Page, from: http://www.passionforpuzzles.com/puzzles/flipside.php
Hungarian circa 1980s?
(plastic, 3.25 inches)
Two openings in the clear outside shell allow fingers to be used to rotate the inner ball. The inner ball has pentagons with holes in them and the outer ball has dots. The goal is to rotate the inner ball so that each dot is inside a pentagon hole.
a.k.a. Rubik's Hat
Matchbox circa 1994.
(plastic, 2.4 inch top, 3.75 inch rim, 3 inches high)
Six discs, each with nine slices, can be rotated. In the initial position, with the letters* R u b i kin a vertical line down the outside, no rabbits are visible when turning over the hat and looking in the bottom with light behind. The goal is to rotate the discs so that nine rabbits, one in each slice, can be seen. Jaap's Page gives an analysis that shows the following solution to be unique (this view looks inside with the rim of the hat facing up):
Further Reading
Jaap's Page, from: http://www.jaapsch.net/puzzles/rubrab.htm
Purchased from Rubik Fans 2007; a similar puzzle is described in the patent of R. Massimiliano 1996.
("Type 1" and "Type 6" puzzles, plastic, 3.25" diameter, 7/8" thick)
On top of the puzzle, eight outer circles and a center circle with ring around it can be rotated (there are no circles on the bottom). There are two dials, one around the edge of the top and one around the edge of the bottom (the center ribbed portion of the puzzle is just for holding it). Internal gears are arranged in a way so that the two dials can rotate different portions of the puzzle. This puzzle has been made with different graphics and different arrangement of internal gears. For example, with the "Type 1" puzzle shown on the left above, the top dial rotates 4 consecutive outer circles and the center ring, and the bottom dial turns rotates all eight outer circles and the center ring / circle combination (also, the entire center platter rotates slowly as the botom dial is rotated).
Jaap's Page describes an Enigma puzzle with an arrrangement of gears that rotate disjoint subsets of circles / rings, and having taken it apart, gives the number of teeth on the gears. The general idea of his solution, which seems to apply to all of these puzzles, is to start by solving a portion and then turn rings a number of times to match up with common multiples of ring revolutions.
Further Reading
Jaap's Page, from: http://www.jaapsch.net/puzzles/enigma.htm
Massimiliano WO Patent, from: www.epo.org - patent no. WO9602307
Presented here are two dimensional sliding piece and manipulation puzzles, including the movement of square pieces (e.g., Fifteen), rectangular pieces (e.g., Traffic Jam), rectilinear shaped pieces (e.g., Neo Black and White), balls (e.g., Hungarian Rings), and tokens (e.g., TeeZ / Brainbuster).
a.k.a. Game of Fifteen, Sliding Numbers, Gem Puzzle, Boss Puzzle, Le Taquin, ...
Old idea dating back at least to circa 1880, this version copyright ThinkFun 2000.
(metal with plastic case, 2.5 inches; keychain 1.75 inches)
Packaged with 1 through 15 arranged by row (lower right empty). After sliding pieces to mix it up, one must return to the starting position. The back of the box says that this one reproduces a 1933 design called the IMP:
To solve, the top two rows are easy, then cycle the last two rows, taking "short cuts" as needed to rearrange the order of pieces in the cycle.
Here are some other problems from the back of the ThinkFun Mini Fifteen keychain. The first, to make a magic square with the empty square counting as 0, is the Spanish Dungeon of H.E. Dudeney 1917 (see Baxter's Page). The last, the reversing problem, is noted as impossible:
Fifteen-Fourteen, plastic, 2.5", circa 1970. A parity argument implies that half the puzzle configurations cannot be reached from any given configuration. For example, the starting position of the Fifteen-Fourteen puzzle shown on the left below has 14 and 15 exchanged, making the standard solution impossible (although as shown on the right below, solution is possible with the empty square in the upper right).
Fifteen-Fourteen, used by J. A. Storer as a child circa 1965.
Here is a proof that the Fifteen-Fourteen problem cannot be solved, based on the presentation on the Wikipedia Page:Define the count of a position to be the number of pairs of pieces that are out of order plus the number of the row that contains the empty square (rows are numbered 1 to 4). The parity of a position is even if its count is an even number and odd otherwise. Moving a piece one left or right does not change the position count since this does not change the ordering of pieces or the row number of the empty square. Moving a piece vertically always changes the position count by 4 because it changes the order with respect to three other pieces and changes the row number of the empty square by 1. Hence, since both 0 and 4 are even numbers, each move preserves position parity, and all positions reachable from a given starting position must have the same parity. Thus, the 1-15 position cannot be reached from the 1-13-15-14 position because these positions have different parity.In general, if you can get to where you have the position you want to reach except that in one place two adjacent squares are exchanged, then that position cannot be reached. For example, if someone gives you a what looks like a fifteen puzzle in a mixed up position, you can try to make the standard 1-15 position and either be successful or arrive at the 1-13-15-14 position (and be certain that this is a Fifteen-Fourteen puzzle for which a 1-15 solution is not possible). As another example, the reversing problem is not solvable, because it is possible to get to an almost reversed position except that the 1 and 2 are exchanged, as depicted below:
Old versions of the fifteen puzzle typically had pieces that could be removed, and sometimes a piece 16 was included that was not used to play the normal fifteen puzzle, or left in for making a magic square, of the numbers 1 to 16, defined as an arrangement so that the four rows, the four columns, and the two diagonals all sum to 34. One example is the Boss puzzle shown on the next page, which refers to this as the "Thirty Four" problem. Here is another:
Le Taquin, manufactured by JJE Paris, circa 1880's?
(wood box and 16 wood pieces, 3.9 by 3.9 by 3/4 inches;
shown on page 61 of the Fifteen book,
the French directions on the inside top cover describe both 15 and magic square)
The idea of magic squares dates to over a thousand years ago; here are two old designs shown on the Wikipedia page:
The Winning Ways book (page 778-783) discusses the design of 4x4 magic squares and notes that the 880 ways to do it for the numbers 1 to 16 (not counting reflections and rotations) was worked out in 1693 by Frenicle de Bessy; see also the Wolfram Mathworld page.
BOSS THE NEW GAME OF FIFTEEN, W. H. Cremer, London, 1880.
(cardboard box and 16 wood pieces, 3.5 by 3.5 by 5/8 inches;
15 diagram on underside of the box top, and 17 page booklet about the 34 puzzle;
similar to the puzzle shown on page 73 of the Fifteen book)
This clipping was tucked into a copy of the 1893 Hoffmann book; from the text on the reverse side, it appears to be from a February 13, 1880 issue of an Albany newspaper.
--- 636 --- IMP - On Which the ThinkFun Version Was BasedShown on page 102 of the Fifteen book. This 2.5 inch square metal puzzle was made in the 1933 to 1934 time frame in a number of similar variations, including different pegs on which the pieces slide (round vs. square), different colors, different text on the sides of the puzzle, different cases (shiny vs. textured red), similar but different booklets (all are 2.25 inches square with the same cover graphics), and even a braille version.
round pegs with black and white tiles,
bottom edge says
MADE IN U.S.A.,
left edge says
"IMP" PAT. APPLIED FOR,
right edge says
MODERN BRANDS INC. N. Y.,
top edge is blank
square pegs with black and white tiles,
bottom edge says
"IMP" PAT. APPLIED FOR MADE IN U.S.A.,
top edge says
MODERN BRANDS INC. N. Y.,
other edges are blank
square pegs with black and red tiles,
bottom edge says
"IMP" PAT. APPLIED FOR MADE IN U.S.A.,
top edge says
MODERN BRANDS INC. N. Y.,
other edges are blank
square pegs with black and red tiles,
bottom edge says
"IMP" PAT. APPLIED FOR,
top edge says
IMPORTED BRANDS INC. N. Y.,
left and right edges are blank
square pegs with red and white tiles,
bottom edge says
"IMP" PAT. APPLIED FOR,
top edge says
IMPORTED BRANDS INC. N. Y.,
left and right edges are blank
square pegs with blue and white tiles,
bottom edge says
"IMP" PAT. APPLIED FOR,
top edge says
IMPORTED BRANDS INC. N. Y.,
left and right edges are blank--- 637 --- IMP 1934 Booklet - Modern Brands
(from the black & white round peg MODERN BRANDS version shown above)
--- 638 --- IMP 1933 Booklet - Modern Brands
(from the black & white square peg MODERN BRANDS version shown above)
--- 639 --- IMP 1933 Booklet - Party Bridge Play Inc.
(from the black & red square peg IMPORTED BRANDS version shown above)
--- 640 --- IMP Undated Booklet - Imported Brands Inc.
(from the blue & white square peg IMPORTED BRANDS version shown above)
Many fun and promotional versions of the Fifteen puzzle have been made with graphics of some kind rather than numbers. Sometimes the graphics are such that every square is unique, and so it is really exactly the same puzzle as the standard Fifteen. However, when there are two pieces that are identical, as is the case with each of the four Warner Brothers puzzles shown below, it is possible to be stuck at a configuration where the puzzle is finished except that two adjacent pieces are out of order. In this case, solve the puzzle with the positions of the two identical pieces exchanged. For example, for the bugs bunny puzzle shown below, the pieces that go in positions 5 and 9 are identical (note that this is not the case for positions 8 and 12 because piece 12 is not quite blank); if you are not able to complete the last two rows because of this problem, move the blank piece that appears to go in position 9 to position 5 (causing the blank piece that was in position 5 to now be in the last two rows), and now solve the last two rows.
Bugs Bunny, Warner B. 1979.
(plastic, 4.8 by 3.9 inches)
Bugs Bunny / Daffy Duck, Warner B. 1979.
(plastic, 4.8 by 3.9 inches)
Road Runner, Warner B. 1979.
(plastic, 4.8 by 3.9 inches)
Tweety, Warner B. 1979.
(plastic, 4.8 by 3.9 inches)
Roalex Co., Forest Hills, NJ, circa 1950's and 1960's.
(card is 4.4 by 5.6 inches, puzzle is plastic 2.5 inches by 1/4 inch thick)
Roalex Co., Forest Hills, NJ, circa 1950's and 1960's.
(card is 5 by 6 inches, puzzle is plastic 2.5 inches by 1/4 inch thick)
The Roalex Co. made numerous Fifteen puzzles based on cartoons and TV shows; some based four related characters in each of the columns (such as the popeye puzzle above) and some on individual characters (such as the Superman puzzle above that J. Storer played with as a child). These puzzles on their original cards (which sometimes had an extra piece on top) are a popular for collectors (see further reading).
Gem Puzzle No. 0, Matthias Rice, December, 1879.
(3.25 inches square by 1/2 inch thick cardboard box and 15 wood pieces;
shown on the cover page, page 8, and page 11 of the Fifteen book,
which dates this puzzle and gives some history)
The top of the box top says "THE GEM PUZZLE No. 0", the bottom of the box top says "Place the Blocks in the Box irregularly, then move until in regular order.", the left and right sides have been scratched out on this one, but originally on the left side was "MANUFACTURED BY M. J. RICE" and on the right side "For CARY, FULTON & Co., No. 29 Kingston Street, Boston."
Although the theme of the Fifteen book is that the origin of the Fifteen puzzle is unknown, it does indicate that the high popularity of the puzzle in the 1880 time frame started with this production of the puzzle in December of 1879, and describes a March 1, 1880 interview of Mr. Rice published in the Boston Herald that describes how he got the idea for making the puzzle from a version made in Hartford by deaf students, and sold for 75 cents apiece.
Wm. F. Drueke & Sons, Grand Rapids, Mich.", circa 1960's.
(plastic, 2.5 inches square by 3/16 inch thick)
Rudolph Steiner, NY, circa 1950's.
(cloth pouch, plastic puzzle, and cardboard instructions, 2.5 inches;
the back says THE "15-PUZZLE", ARRANGE NUMBERS. HORIZONTALLY, VERTICALLY,
DIAGONALLY, OR IN SPIRALS, ETC., PAT. APPLIED FOR, RUDOLPH STEINER CO., N.Y.C. U.S.A.)
Lowes, 1950's.
(felt lined pouch, plastic puzzle, and cardboard instructions, 2.5 inches;
shown on page 103 of the Fifteen book)
Lowes, circa 1940?
(4.75" square by 1" leather covered box with fifteen 1" square by 1/2" wood pieces)
Wood box with inlay of dancing couple and 15 wood pieces, 1837 ???
(4.6 inches square by 1 inch thick, pieces are 1 inch square by 1/4 inch thick,
the date 1837 is hand written on the back)
This box has a beautiful inlaid top showing a dancing couple and looks quite old. The date of 1837 written on the back raises the fun possibility that this puzzle pre-dates the 1880's Fifteen puzzle craze that is documented in the Fifteen book. However, it is hard to give this date too much weight; it could have been written by anyone at anytime. Below are photos of the inside, which looks quite similar (including the hinges) to the inside of the Souvenir d'Egypt puzzle (made in France) that is shown on page 97 of the Fifteen book.
Calculator Puzzles, England, circa 1880's.
(4.5" square by 7/8" wood box and sixteen 1" diameter by 3/8" painted wood pieces;
paper label on box top and rules on underside of box top;
same box as the one shown on page 25 of the Fifteen book.
Little Buttercup puzzle, B. F. Gould, 40 Bromfield St., Boston, 1880.
(cardboard box and 15 wood pieces, 3 by 3 by 1 inch;
the ridged tops have the numbers 1-15 and the smooth bottoms have letters
(close-ups of the piece P / 5 are shown above),
the directions on the box top ask you to spell LITTLEBUTTERCUP
(the fourth T and the C are a too worn to read in the photo above),
the Fifteen book shows this puzzle on pages 20, 36, and 49
where it credits manufacture to B. F. Gould and shows a Feb. 1880 advertisement)
Hopkins, circa 1880's.
(wood tray and 15 wood pieces, 3.7 inches;
1 is a bit burned, 5 is damaged, and 10 was lost and replaced by a blank,
the back is stamped "J. A. Hopkins MAKER Oxford NY",
from J. A. Storer's grandfather in Oxford NY)
The Game of Fifteen Gem Puzzle, manufactured by Alan L. Lovejoy, Boston, 1880.
(cardboard box. wood tray, and 15 wood pieces, 3.75 by 3.75 by 3/4 inches;
shown on page 19 of the Fifteen book where it cites manufacture and date)
The Game of Fifteen Gem Puzzle, circa 1880.
(cardboard box. wood tray, and 15 wood pieces, 3.75 by 3.75 by 3/4 inches;
shown on page 23 of the Fifteen book)
Double Puzzle Of Crack Brain And Thirty Four, Heyer Brothers, Boston, circa 1880.
(cardboard box, wood tray, and 16 wood pieces, 3.9 by 3.9 by 3/4 inches;
directions on the inside of the box top;
shown on page 40 of the Fifteen book.
The Gem Puzzle / Double Puzzle, circa 1880's.
(cardboard box and 16 wood pieces, 3.25 inches square by 9/16 inches;
shown on page 34 of the Fifteen book;
includes piece 16 to have the magic square as a second puzzle)
The Boston Puzzle, circa 1880's.
(cardboard box and 15 wood pieces, 3 inches square by 5/8 inches;
different than the "Boston Puzzle" shown on page 24 of the Fifteen book)
The Puzzle Of 15 and 16, circa 1880's.
(cardboard box and 16 wood pieces, 3.25 inches square by 51/2 inches;
shown on page 38 of the Fifteen book;
"This little puzzle looks simple and easy but TRY IT ONCE.";
this one came with an article from a 1926 newspaper that reflects on the Fifteen Puzzle
as something from the past when R. B. Hayes was president)
The Popular Fifteen Puzzle, F. Passmore, London, circa 1880's.
cardboard box and 15 wood pieces, 4.2 inches square by 5/8 inches;
directions on the inside of the box top;
On page 30 of the Fifteen book, but with a different English manufacture;
a very similar box top is also shown inside the cover of the Fifteen book)
German, circa 1880's.
(cardboard box and wood pieces, 2.5 x 2.5 x 3/8 inches;
shown on page 121 of the Fifteen book)
On the page of the Fifteen book that shows this puzzle is a nice discussion of how newspapers from February and March of 1880 had a large number of "notes, articles, and poems that claimed that the Fifteen Puzzle was driving solvers insane and overcrowding the lunatic asylims".
Fifteen Puzzle, Spear Works Bavaria 1915.
(cardboard box and wood pieces, 4 x4 x 5/8 inches;
shown on page 119 of the Fifteen book where it cites manufacture and date)
Gem Puzzle by John Heywood, Manchester, UK, undated.
(cardboard box and 16 wood pieces, 3.4 x 3.4 x 1/2 inch,
shown on page 29 of the Fifteen book)
15 and 34 puzzle, De La Rue & Co., London, circa 1880.
(cardboard box. wood tray, and 15 wood pieces, 3.75 by 3.75 by 5/8 inches;
shown on page 35 of the Fifteen book)
King George VI Coronation Puzzle, circa 1937.
(cardboard box and 16 cardboard pieces, 4.25 x 4.25 x 1/4 inch;
inside of box top has directions;
inside of the box bottom advertises Meadow Butter;
both the puzzle pieces and the box top have photos of the royal family; to read about king George VI, see for example
the King George VI Wikipedia Page,
from: http://en.wikipedia.org/wiki/King_George_VI )
15 Puzzle, The Embossing Company, Albany, NY, circa 1937.
cardboard box and 15 wood pieces, 4.2 x 4.2 x 5/8 inch;
this red version appears to have a second 6 instead of a 9,
same manufacturer and box size / style as the Time and Missionary Puzzles)
The Combination Puzzling Puzzles, copyright Canada 1934.
(wood box, 15 wood pieces, 3.9 by 3.9 by 7/8 inches;
flip the puzzle over and the backs of the pieces have the letters GDOAETYNANALNI?,
? for piece 13 that has been replaced and had A hand written on the back)
Adams Co., unknown age.
(cardboard case and metal puzzle, 3.25 inches)
Dukes Of Hazzard, Warner B. 1981.
plastic, 4.8 by 3.9 inches
Bo, Luke, Daisy Duke, Warner B. 1981.
plastic, 4.8 by 3.9 inches
Boss Hogg, Warner B. 1981.
plastic, 4.8 by 3.9 inches
General Lee, Warner B. 1981.
plastic, 4.8 by 3.9 inches
Superman, D C Comics 1978.
(plastic, 4.8 by 3.9 inches)
Spiderman, D C Comics 1978.
(plastic, 4.8 by 3.9 inches)
Popeye, King Features 1981.
(plastic, 3.5 by 3 inches)
101 Dalmations, Disney, circa 1960's?
(plastic, 3.5 by 3 inches)
Circa 1960's.
(brass, 3.25 inches)
Hungarian, circa 1950?
(metal, 2.75 inches)
The Monitor, Artist Series, Philips, no date.
(plastic, 3.5" x 2.9" x 1/4";
sticker on back shows solved position)
Circa 1960's.
(plastic, 2.5 inches)
Marge & Homer Simpson, circa 2000.
(plastic, 2.5 inches)
Bart Simpson, circa 2000.
(plastic, 2.5 inches)
Examples of Roalex Puzzles For Sale
Slocum's Page, from: http://www.puzzleworld.org/PuzzleWorld/jerry_slocum.htm
Baxter's Page, from: http://www.johnrausch.com/SlidingBlockPuzzles/15.htm
Jaap's Page, from: http://www.jaapsch.net/puzzles/fifteen.htm
Wikipedia Fifteen Page, from: http://en.wikipedia.org/wiki/Fifteen_puzzle
Wikipedia Magic Square Page, from: http://en.wikipedia.org/wiki/Magic_square
Wolfram Magic Square Page, from: http://mathworld.wolfram.com/MagicSquare.html
May Patent, from: www.uspto.gov - patent no. 50,608
Kinsey Patent, from: www.uspto.gov - patent no. 207,124
McCleary Patent, from: www.uspto.gov - patent no. 284,037
Brown Patent, from: www.uspto.gov - patent no. 390,829
Bradshaw Patent, from: www.uspto.gov - patent no. 427,392
Brown Patent, from: www.uspto.gov - patent no. 433,444
Cook Patent, from: www.uspto.gov - patent no. 476,980
Anderson Patent, from: www.uspto.gov - patent no. 483,276
Eymann Patent, from: www.uspto.gov - patent no. 535,279
Johnson Patent, from: www.uspto.gov - patent no. 1,555,980
Fritz Patent, from: www.uspto.gov - patent no. 1,693,711
Nesis Patent, from: www.uspto.gov - patent no. 5,785,318
a.k.a. Fifteen Puzzle
Basic idea dates to before 1900, this Escher drawing purchased 2007.
(plastic, 3.6 by 2.9 inches)
Like the Fifteen puzzle puzzle except there are sixteen pieces and a seventeenth extra space. The piece adjacent to the extra space in the solved position will always either be there (in which case no pieces can move until it is moved into the extra space) or be in the extra space. So this puzzle can be solved by first placing this piece in the extra space, solving the remaining Fifteen puzzle, and then moving this piece back. The position of the extra space does not matter, and varies from one puzzle to another. Here's one with the extra square by the upper right corner:
Flintstones, circa 1965?
(plastic, 3.6 by 2.9 inches)
Further reading:
Larabee Patent, from: www.uspto.gov - patent no. 1,477,371
Green Patent, from: www.uspto.gov - patent no. 2.007.530
Feller Patent, from: www.uspto.gov - patent no. 5,529,301
A smaller version of the Fifteen Puzzle.
Alien, DaMert Co. 1993.
(plastic, 4 inches)
Praying Mantis.
(plastic, 3 inches)
Lisa Simpson.
(plastic, 1.9 inches)
Maggie Simpson.
(plastic, 1.9 inches)
The 1985 patent of Morrone shows a version of the Nine Puzzle where instead of a missing square there are 9 pieces and an extra tenth position into which one can be slid so the others can move around like the standard Nine Puzzle; the patent also defines the object of the puzzle to arrange the pieces so that the numbers add to 15 in all directions. Below is an add for Phenyo Caffein (which was tucked into the pages of the green cover version of the 1893 Hoffmann book by some previous owner) that presents a 3x3 magic square puzzle. This puzzle is also shown on the back of the solution to the Misfit Puzzle (which was sold by Phenyo Caffein).
Further reading:
Morrone Patent, from: www.uspto.gov - patent no. 4,548,410
a.k.a. Fourteen Puzzle
PLAS TRIX CO., Brooklyn, NY, 1950.
(soft plastic case, cards, and two 2.5 by 3.75 inch puzzles)
Similar to the Fifteen puzzle; use one puzzle to try to make different patterns (e.g., 1 to 14 in numerical order), or two puzzles to race an opponent to make patterns specified by the playing cards. Here are the front of the card box, the back of each playing card, the text from the back of the card box, and the front and back of the instructions card:
Craig Biscuit Co., Fort Wayne, Indiana, unknown age.
(cardboard box 4" by 4" by 1/2" and 16 wood pieces)
Make a magic square where all rows, columns, and diagonals add to 50. This is in a theme similar to many versions of the Fifteen puzzle that include a 16th square so that one can make a magic square based on summing to 34.
Further Reading
Wikipedia Magic Square Page, from: http://en.wikipedia.org/wiki/Magic_square
Wolfram Magic Square Page, from: http://mathworld.wolfram.com/MagicSquare.html
Copyright S. S. A. Co., 1915.
(1.75"x4.75"x7/16" cardboard box and 12 wood pieces with paper glued to top;
directions are on the inside of the box lid)
Starting with the P and C exchanged, slide the pieces to put them back.
A parity argument (like that for the Fifteen puzzle) might lead one to think that a solution is not possible. However, the second and fourth squares of PANAMA can be exchanged without significantly changing the look of the picture formed by the pieces (if one ignores the background graphics, then shorter solutions are possible - see next page).
Panama Canal: Here is a 32 move solution, where 1, 2, 3, 4, 5 represent the five A's, and X, Y represent the two N's. If a piece can push other pieces, then this solution can be converted to 21 moves by combining steps 1/2, 8/9/10, 12/13/14, 16/17, 21/22, 28/29/30/31/32.
Panama Canal NB: For the simpler problem with no background, here is a 26 move solution. If a piece can push other pieces, then this solution can be converted to 17 moves by combining steps 1/2/3/4, 8/9, 15/16, 22/23/24/25/26.
Panama Canal H: For the even simpler problem with no background and "CANAL" can be right justified, Hordern's book gives a 23 move solution and Baxter's Page lets one search for a 21 move solution. If a piece can push other pieces, then this solution can be converted to 16 moves by combining steps 1/2/3/4, 8/9, 15/16.
Designed and made by J. A. Storer 2007.
(3"x 7" x 1.4" wood box, 11 wood pieces, and a black wood keeper piece)
Panama Canal S: In this version, the second and sixth squares of PANAMA can be exchanged without changing the picture. Here is a 48 move solution. If a piece can push other pieces, then this solution cab be converted to 36 moves by combining steps 6/7, 11/12, 16/17/18, 20/21/22, 24/25, 29/30, 36/37/38/39, 43/44.
This version does a reasonable job of "exercising" the pieces. Since half of the possible positions are duplicates due to the two A's with the same background, there are 12! / 2 = 239,500,800 distinct positions. To find a solution, a computer program performing a simple breadth-first search visited 102,714,408 positions (43 percent). In contrast, the program visited 3,611,235 positions (1.5 percent) to solve the standard version, and for the NB and H versions, where the five A's are interchangeable and the two N's are interchangeable, giving 12! / 5! / 2 = 3,991,680 distinct positions, to find a solution it visited 120,542 positions (3 percent) and 42,602 positions (1 percent) respectively.
The 2-unit high shape has been used in similar puzzles. The 1923 Hartman patent shows the same puzzle but with the numbers 1 to 11 on the pieces (and the goal is to rearrange them so each column sums to 11). The puzzle below, purchased in 2008, has a 2 by 7 array of pieces and an extra position (similar to the Sixteen puzzle):
Further Reading
Baxter's Page, from: http://www.johnrausch.com/SlidingBlockPuzzles/classic.htm
Hartman Patent, from: www.uspto.gov - patent no. 1,464,424
a.k.a. a.k.a. 5-Block Puzzle, Lodging House Difficulty
Very old design, this one made by J. A. Storer 2007.
(cardboard sleeve, 5 by 7 by 3/4 inch wood tray, and five wood pieces)
The problem is to exchange pieces A and B by sliding the pieces::
Presented in the 1914 Loyd book; both the 1942 Filipiak book and the Hordern book present a 17 moves solution (and Baxter's Page lets you play it on-line):
Further Reading
Baxter's Page, from: http://www.johnrausch.com/SlidingBlockPuzzles/classic.htm
a.k.a. Target
Very old design, this one made by J. A. Storer 2007.
(wood box 3.5 by 6.5 by 1.25 inches, 11 wood pieces, and a brass clip;
shown on page 8 of the 1942 Filipiak book)
Hordern's book speculates that this puzzle may have began as a mistake when attempting to make the Get My Goat puzzle; it is the same except that the upper right corner is two pieces instead of a single piece (this version allows one to join these two pieces with a brass clip if one wants to play Get My Goat). The object is to move the red square to the middle by sliding the pieces. The solution of 17 steps below (along with an 18th step to adjust the final position), that is presented in the Hordern book does not use the left three pieces.
Made 1919.
(cardboard box and 11 stone pieces, 2.6 by 3.3 by 7/16 inches)
Below are the directions that came with the puzzle. Hordern's book dates this puzzle, and gives solutions of 27 moves to get the three discs to the center and 28 moves to get them to the bottom (with GOOD LUCK on the first two rows).
Circa 1960's?
(plastic, 20 tiles, 3.4" by 1.5" by 1/4" thick)
Larger version of the Nine Puzzle; can be solved in the same way.
The Embossing Company, Albany, NY, circa 1930;s.
(cardboard box 4.1" x 4.1" x 1/2" and 24 wood 3/4" x 3/4" x 3/8" wood pieces)
A 5 x 5 version of the Fifteen puzzle. Begin with the orange lettering up, solve the crossword puzzle on the orange side of the directions, and slide the pieces to make that pattern. Then turn over the pieces to have the green lettering up, turn the directions over to green side, solve that crossword puzzle, and slide the pieces to make that pattern. On the right above is each piece of the orange solution turned over.
Larger versions of the Fifteen Larger versions of the Fifteen puzzle can be solved the same way; a common example is 27 tiles (see also the 20 and 31 puzzles).
Unknown manufacture.
(wood, 3 by 4.75 by 1.25 inches)
The box can be turned over to play the One To Ten on the other side:
Circa 1960?
(plastic, 27 tiles, 4.7 by 2.9 by 3/16 inch thick)
Circa 1960?
(plastic, 27 tiles, 4 by 2.4 by 3/16 inches)
Requires one to work out a crossword puzzle, Plastrix Co., circa 1950's.
(9" x 7" cardboard card and plastic puzzle 4.9" x 3.1" x 5/16"; solution above from
M. Keith [2011], "Vintage Plastic Sliding-Letter Puzzles" Word Ways 44:4, 310-31)
Larger versions of the Fifteen Larger versions of the Fifteen puzzle can be solved the same way; a common example is double the size with 31 tiles (see also the 20 and 27 puzzles).
a.k.a. Jumble
Archer Plastics, Bronx, NY, circa 1960.
(plastic, 31 tiles, 5 by 2.9 by 1/4 inch thick)
Wm. F. Drueke & Sons, Grand Rapids, Mich.", circa 1960's.
(plastic, 31 tiles, 5.1 by 2.9 by 1/4 inch thick)
"Roalex's Zig-Zaw Puzzle Map of The World", circa 1960s.
(plastic, 31 tiles, 3 by 5 by 5/16 inches;
see the Fifteen puzzle further reading for a photo of the packaging)
Map of the U.S., circa 2000?
(plastic, 31 tiles, 3 by 5 by 3/16 inches)
Wm.F. Drueke & Sons, Grand Rapids, 4, Mich.
(plastic puzzle with 31 tiles 2.9" x 5.1" x 1/4"; directions on the back)
With a computer in 2011, M. Keith identified 299 solutions using valid Scrabble words with the stronger requirement of having no two-letter words; 14 of them use only the first 7 columns (see also M. Keith [2011], "Vintage Plastic Sliding-Letter Puzzles" Word Ways 44:4, 310-31).
The Embossing Company, Albany, NY, circa 1930's.
(4.4"x4.4"x5/8" inch cardboard box and 16 wood pieces; directions inside box top)
Copyright Richard Appel, Inc., NY, 1943.
(2.5"x2.5"x1" cardboard box, 2.4" square board, and eight 13/16" wood cubes;
Described on pages 135-136 of the Hordern book, which dates the puzzle)
Start with the cubes placed on the board according to their color, and then move the purple cube in the upper left corner to the lower right corner in such a way that pieces of the same color never touch each other along a side. The two purple blocks may not touch, but are different shades of purple allow one to keep track of which is the one that started in the upper left.Includes a 24 move solution; Hordern presents a minimal 22 move solution:
G Y O Y G P Y O P G O G O Y G P Y O P G Y P
a.k.a. Slide-Blocked Sliding Block
Designed by B. Cutler 1988, made by T. Lensch 2007.
(laser engraved wood, 7.5 by 5.5 by 3/4 inches)
The 5 unit size blocks slide in the tray and can't be removed due to interlocking edges. The edges are formed in a way that not all sliding motions are possible at any given time. The goal is to move Grandpa's car from the right to the left. The edges are such that the left door top / window bottom cannot slide above the car, and hence the middle two squares must be exchanged. By the same parity argument as for the Fifteen Puzzle Puzzle, this implies that the top two squares must also be exchanged. Hence, the puzzle is:
This puzzle is bit harder than the Moving Day puzzle but not too hard. The sheet that was sold with the puzzle gives the following solution of 41 moves; here we use a letter to denote moving the corresponding piece and a number to repeat the group in parentheses that many times:
(Y X A B G)3 Y B A X B Y G A Y B X Y A G B A (G B A X Y)2
Patented by T. Graham 1934, made by the Embossing Company of Albany 1937.
(cardboard box 4.4" x 4.4" x 5/8" inches and 13 wood pieces;
Hordern's book dates the blue version above as made in 1937, and gives a solution)
Slide the pieces, avoiding the two forbidden squares, to get go from a start position to a final position; here are problems 1, 2, and 3 from the directions that were sold with it:
Further Reading
Graham 1934 Design Patent, from: www.uspto.gov - patent no. Des93,344
Graham 1935 Patent, from: www.uspto.gov - patent no. 1,989,411
a.k.a. Motor Garage Puzzle, Parka Car, Sputnik Puzzle, E Peg Puzzle
Designed by H. E. Dudeney 1910, made by Binary Arts circa 2000.
(metal with plastic case, 2.5 inches)
Slide the pieces to exchange "WORK" and "GOLF":
Presented in Dudney's 1917 book Amusements in Mathematics as the Motor Garage Puzzle, which also presents the smaller Motor Car Puzzle; both of these puzzles can be played on-line on Baxter's Page. McFarren's Page presents a step by step solution. Hordern's book credits Dudney's 1910 submission to the Strand Magazine. Here is the 43 moves (85 straight-line moves) solution from page 27 of the 1942 Filipiak book (steps 6 and 7 have been corrected and letters are used instead of numbers to the left of arrows):
Further Reading
Work Or Golf Solution Steps (43 rectilinear, 85 straight-line, 150 unit)
Work Or Golf Solution Steps (43 rectilinear, 83 straight-line, 154 unit)
McFarren's Page, from: http://www.geocities.com/abcmcfarren/math/golf.htm
Baxter's Page, from: http://www.johnrausch.com/SlidingBlockPuzzles/classic.htm
DeVos Patent, from: www.uspto.gov - patent no. 4,097,049
a.k.a. Black And White
Copyright Binray Arts 2002;
originally "BLACK and WHITE" by K. Wells in Popular Mechanics 1971.
(metal, 1.75 by 3 inches)
Hordern's book Hordern's book gives a 62 rectilinear moves (85 straight-line moves) solution for the BLACK and WHITE version; starting with the figure on the right above, here are the positions resulting from the 23 non-straight-line moves, and the final position:
a.k.a. Katch the Kaiser, Katch The Kron Prinz, ...
Patented by J. Wiley 1914.
(left: 2.9 by 3.75 by 7/16 inch cardboard box and 11 wood pieces 1/4" thick;
right: 2.9 by 3.75 by 3/8 inch cardboard box and 11 cardboard pieces 3/16" thick;
both box tops say "OFFICE 1058 BROAD ST. PROV. R.I. PAT. OCT. 6, 1914";
solution sheet of the red version says "Rust Craft Publishers, Inc., Boston, MA.";
shown on plate 6 of Hordern's book and page 134 of the Fifteen book;
similar to but a bit harder than the Bull's-Eye puzzle)
There are one 1x2 piece (in the upper right of the starting position), nine 1x1 pieces, and 1 keeper piece (center of the starting position). Both box tops have the same directions on the underside, that instruct one to move the goat to the middle:
Inlaid Company, Providence, R.I., patented October 6, 1914.
(2.9 by 3.75 by 3/8 inch cardboard box and 11 cardboard pieces 3/16" thick)
"BRITISH MADE, Patent No. 14356/16 Appd. for."
(2.9 by 3.75 by 3/8 inch cardboard box and 11 cardboard pieces 3/16" thick)
Further Reading
Baxter's's Page, from: http://www.johnrausch.com/SlidingBlockPuzzles/classic.htm
Wiley Patent, from: www.uspto.gov - patent no. 1,112,746
The Embossing Company, Albany, NY, 1934.
(cardboard box 3.5 by 5.4 by 1/2 inches and ten wood pieces;
described on page 70 of the Hordern book, where it is dated and
credited as named to celebrate the birth of the Dionne quintuplets;
same manufacturer and box style as the Fifteen, Time, and Missionary Puzzles)
Line up the Quinties in the center row from the specified starting position; the directions are shown on the next page; here are diagrams of positions 0, 4, 8, 12, 16, 20, 25, 30 of the Hordern book solution of 30 rectilinear moves (equal to 33 straight-line moves):
Southern Toy Co. for Long Sales Co., Johnson City, TN, circa 1930's?
(wood box that looks like a book and 7 wood pieces, 8.5" x 6" x 5/8")
Exchange the dark and light pieces; here are selected positions of a not minimal 42 rectilinear moves solution (59 straight-line moves):
Starting with move 15 of the solution of the previous page (step 5 of the selected steps shown), here are different additional steps that can be taken to achieve a 39 rectilinear moves solution:
Here is the full 39 moves rectilinear move solution (59 straight-line moves):
Here is a 58 straight-line moves solution (41 rectilinear moves):
Designed by Serhiy Grabarchuk, made by J. A. Storer 2007.
(4" x 4" x 3/4" wood tray, 7 wood pieces, and black plexiglass keeper)
Move all the pieces clockwise one unit:
Baxter's Page lets you play this puzzle on-line to try to find the 31 move minimal length solution.
Further Reading
Baxter's Page, from: http://www.johnrausch.com/SlidingBlockPuzzles/serhiy.htm
These were a series of cardboard puzzles (see the following pages for examples) that came in a fold-out mail envelope; presumably an inexpensive amusement that could be mailed to a friend or family member. They are based on 1x1 and 1x2 pieces on a 3 x 5 unit board. For example, here is the problem of the "Tank Attack" puzzle (shown on the next page):
The instructions for Tank Attack, like other puzzles in the series, show a filler piece no. 1 for the 2 x 1 empty space, call it a move to remove this piece and replace it at the end, and give a solution of 24 straight-line moves that includes these two moves. However, this solution is referred to as 22 moves. So we won't count those two extra moves her either. Also like other puzzles in the series, the instructions for Tank Attack pose the simpler problem of moving piece 4 to the lower right without regard to where the other pieces end up. Here is a 13 straight-line move solution to do that (or 11 rectilinear moves by combining steps 1 and 2 and combining steps 4 and 5); in the steps below, 0 denotes piece 10:
Electric Corporation Of America, Chicago, Copyright 1942.
(paper envelope and cardboard puzzle, 4.4" x 6.3")
Electric Corporation Of America, Chicago, Copyright 1942.
(paper envelope and cardboard puzzle, 4.4" x 6.3")
Electric Corporation Of America, Chicago, Copyright 1942.
(paper envelope and cardboard puzzle, 4.4" x 6.3")
Designed by Stewart Coffin 2005; this one made by J. A. Storer 2011.
(Walnut and Cherry with paper piece labels, 4" x 4" x 3/4")
Slide the pieces to fix the caterpillar and butterfly. Below are every 5th move of a 39 rectilinear (51 straight-line) moves solution. Solving for the order caterpillar - butterfly - Monarch can also be done in 39 rectilinear (50 straight-line) moves, and 39 rectilinear (51 straight-line) moves suffice to go between these two solutions.
a.k.a. Dad's Puzzle, Moving Puzzle, Tit-Bits Teaser No. 1,
Penant Puzzle, Box of Nine, Nine Block Puzzle
Patents and copyrights include L. W. Hardy 1909, J. W. Hayward 1926,
Frederic E. Aaron 1927, and C. O. Luce 1953, these two are not dated.
(cardboard box and 9 wood pieces, 4 by 3.25 by 1/2 inches;
presented on pages 78-79 and plate 6 of Hordern's book)
Slide the 2x2 piece from the upper left to the lower left (without picking up pieces); the positions of the other pieces don't matter:Perhaps the most produced mechanical puzzle of the first half of the 20th century, after the Fifteen puzzle. Many were made with the same 4 x 3.25 x 1/2 inch box, the same size and shaped pieces (sometimes plastic in later years), but with additional text or different cover art to promote products (laundry detergent, glue, etc.). See also the Humdinger version.
Here is a solution of 62 straight-line moves; it can be converted to 59 rectilinear moves by combining steps 6/7, 27/28, and 58/59:
(one move = sliding one piece any number of units in one direction)
The diagonal version of Dad's Puzzler is to move the 2x2 piece diagonally to the lower right corner; it is described on page 5 of the 1942 Filipiak book (which gives a solution of 59 moves).
(Move the 2x2 to the lower right; the positions of the other pieces do not matter.)
One might think that it would be a harder to move the 2x2 piece diagonally to the lower right corner since it is farther away than the lower left. However, here is a solution of only 31 straight-line moves; it can be converted to 29 rectilinear moves by combining steps 6/7 and 18/19:
(one move = sliding one piece any number of units in one direction)
Note: For harder versions of Dad's Puzzler where there are additional constraints on the final position, see Dad's Puzzler Exchange.
Tit-Bits Teaser, George Newnes, London, Made in the U.S.A., 1927.
(cardboard box, 9 wood pieces, 4 by 3.25 by 1/2 inches;
page 78 of Hordern's book list this as "Tit-Bits Teaser No. 1, 1927")
Moving Puzzle, Copyright Frederick E. Aaron 1927.
(cardboard box, 9 wood pieces, and solution sheet, 4 by 3.25 by 1/2 inches;
left: blank near the bottom where promotion text usually goes;
right: vendor sample version)
Eskimo Pie Co., "ELGIN ICE CREAM", circa 1940's?
(cardboard box and 9 wood pieces, 4 by 3.25 by 1/2 inches;
directions on inside of box top and solution sheet included;
different versions different Ice Cream distributor on the box top)
Copyright J. W. Hayward 1926,
manufactured by the Standard Trailer Company, Cambridge Springs, PA,
distributed by S-M News Co., Inc., 229 Fourth Ave., New York, NY.
(cardboard box and 9 wood pieces, 4 by 3.25 by 1/2 inches)
Here are the top / bottom (left below) and left / right (right below) box edges:
Here are the directions:
Copyright Standard Trailer Co. 1953.
(cardboard box and 9 plastic pieces, 4 by 3.25 by 1/2 inches)
Cross Publishing, Copyright 1957.
(cardboard box and 9 plastic pieces, 3.25 by 4 by 5/16 inches)
Dads Move A Block, unknown date.
(5.5 by 4 by 1.125 inch high wood box with wood pieces)
C. O. Luce 1953, purchased by J.A. Storer as a child circa 1962.
(cardboard box and 10 plastic pieces, 4 x 3.25 x 1/2 inches)
Adams Company, circa 1930.
(heavy metal tray and lid with nine metal pieces, 4 x 3.25 x 1/4 inches,
paint in bad condition but the pieces slide well with a nice fit;
a newer version is shown on page 62 of the Adams Co. History book)
Adams Company, 1961.
(metal tray and nine plastic pieces, 3.75 x 3 x 5/16 inches;
shown on page 108 of the Adams Co. History book)
Came with solutions to both Dad's Puzzler and Dads Puzzler Diagonal:
Leech Products Co., Hutchinson, Kansas, unknown age.
(cardboard box and 9 wood pieces, 3.5 by 2.8 by 5/16 inches;
direction on inside of box top)
Piedmont Premium Beer., undated.
(cardboard box and 9 wood pieces, 4 by 3.25 by 9/16 inches)
Frigidaire Jumble Puzzle, undated.
(cardboard box and 9 cardboard pieces, 3 by 2.5 by 5/16 inches)
Magnetic Square Puzzle,
WM. F. Drueke & Sons, Inc., Grand Rapids, MI, copyright 1961.
(plastic pieces with magnetic backs in cardboard box with metal bottom,
7.8 by 7.8 by 5/8 inches)
Kasko Puzzler, "REG US PAT OFF".
(cardboard box and 9 wood pieces, 4 by 3.25 by 1/2 inches)
MOVING Puzzle, Copyright Frederick E. Aaron 1941,
"Hasley Bros. MOVING AND STORAGE", Pittsburgh, PA.
(cardboard box and 9 wood pieces, 4" x 3.25" x 1/2"; directions inside box top)
Moving Puzzle, Copyright Frederick E. Aaron 1927,
"GREYVAN STORAGE, INC. 1665 Main St., Buffalo 8, N.Y.".
(cardboard box and 9 wood pieces, with solution sheet, 4 by 3.25 by 1/2 inches)
Motor Grinding Co., copyright J. W. Hayward 1926.
(cardboard box and 9 wood pieces, 4 by 3.25 by 1/2 inches;
directions on inside of the box top)
F. C. Bellis Independent Oil, patent applied for, copyright J. W. Hayward 1926.
(cardboard box and 9 wood pieces, 4 by 3.25 by 1/2 inches;
2x2 piece has paper label; directions on inside of the box top)
Ohio Table Pad Co., copyright J. W. Hayward 1926.
(cardboard box and 9 wood pieces, 4 by 3.25 by 7/16 inches)
Some More Examples Of Dad's Puzzles
Hardy Patent, from: www.uspto.gov - patent no. 1,017,752Filed Dec. 14, 1907; granted Feb. 20, 1912.Kuczynski Patent, from: www.uspto.gov - patent no. 6,039,318
Shows as its preferred embodiment (Figure 1) a 4x4 tray with ten pieces
(one 2x2, three 1x2, two 2x1, and four 1x1).
Claims 8 and 9 addresses a general class of sliding block puzzles with three sizes of pieces,
and Claim 10 addresses puzzles with one 2x2 piece,
some number of 1x2 and 2x1 pieces, and some number of 1x1 pieces.Filed Mar. 4, 1998; granted Mar. 21, 2000.
Figures show Dad's Puzzler and specifications describe a frame for holding it.
Circa 1930's.
(cardboard box and 9 wood pieces, 4" x 3.25" x 1/2")
Move the 2x2 piece from the lower right to the upper right (without picking up pieces). Turn the puzzle upside-down and it is identical to the Dad's Puzzler except that the 1x1 pieces are shifted right 2 units. The inside of the cover has a 5 page pamplet glued to it:
Since the first two moves of the solution presented for Dad's Puzzler are to move the two 1x1 pieces right, a Humdinger solution can be formed by skipping positions 0 and 1 of the Dad's Puzzler solution, giving 60 straight-line moves that can be converted to 57 rectilinear moves by combining steps 4/5, 25/26, and 56/57:
(one move = sliding one piece any number of units in one direction)
U Try It, circa 1930's.
(cardboard box and 9 wood pieces, 5" x 4" x 3/4")
Here is what the directions on the box say:
"Place the blocks as per the above chart and, by
sliding without removing or turning them,
you must get No. 9 to the position of 7 and 8."
Unknown age (sleeve with directions added by J. Storer 2007).
(cardboard sleeve, stained pine tray, 9 walnut pieces, 5.5" x 4.75" x 1.25",
the 2x2 piece is made by gluing two 1x2 pieces together,
the 2x2 has a metal tack on each side and the other have on in the middle,
pencil markings on the tray show a Humdinger start position,
sleeve also has directions for Nine Block, Quzzle, and Quzzle Killer)
New Deal, circa 1930's.
(cardboard box and 9 wood pieces, 3.4" x 4.1" x 1/2")
Further Reading
New Deal Wikipedia Page, from: http://en.wikipedia.org/wiki/New_Deal
"Infants' Hospital Puzzle", Chad Valley Co. Ltd., Harborne, England, 1920;
made for the Infants Hospital in Vincent Square, London, founded by R. Mond.
(cardboard box and 9 cardboard pieces, 6.2 by 5.2 by 1/2 inches;
same hospital, but different puzzle than the better known Infants Hospital Puzzle, and different than the dexterity puzzle A Ward Oin The Infant's Hospital)
This is an example of a version of "Dad's Puzzler". where the directions give additional constraints on the final position; see the following pages.
Further Reading
Infants Hospital History, from: http://ezitis.myzen.co.uk/westminsterchildrens.html
Robert Mond Wikipedia Page, from: http://en.wikipedia.org/wiki/Robert_Mond
The directions to the puzzle on the preceding page say one must not merely move the 2x2 piece to the lower left as with the standard Dad's Puzzler, but it must be exchanged with the two pieces there. Here are a number of interpretations of what this means:
Dad's Puzzler
2x2 Piece must be moved to the lower left corner; no other requirements.
Dad's Puzzler Exchange
2x2 Piece must be moved to the lower left corner; pieces 7 and 8 must move to the upper left corner and may be exchanged.
Dad's Puzzler Exchange-Strict
Exchange upper left 2x2 with lower left pair; the two lower left pieces must remain in same relative order; other pieces do not matter.
Dad's Puzzler Exchange-Full
Exchange upper left 2x2 with lower left pair; the two lower left pieces may be exchanged; other pieces must stay the same or be equivalent.
Dad's Puzzler Exchange-Full-Strict
Exchange upper left 2x2 with lower left pair; the two lower left pieces must remain in same relative order; other pieces must stay the same or be equivalent.
Dad's Puzzler Exchange-Full-Strict-All
Exchange upper left 2x2 with lower left pair; the two lower left pieces must remain in same relative order; other pieces must stay the same and cannot be exchange with equivalents.
The minimal length solution for the standard version (62 straight-line moves, 59 rectilinear moves) also works for the excange version. When the exchange must be strict, here is a 67 straight line moves solution; it can be converted to 65 rectilinear moves by combining steps 6/7 and 63/64:
Here is a 64 straight line moves solution; it can be converted to 61 rectilinear moves by combining steps 6/7, 27/28, 58/59:
Here is a 69 straight line moves solution; it can be converted to 67 rectilinear moves by combining steps 6/7, 63/64:
Here is a 167 straight line moves solution; it can be converted to 165 rectilinear moves by combining steps 6/7, 161/162:
(continued on the next page)
Here is a 167 straight line moves solution; it can be converted to 165 rectilinear moves by combining steps 6/7, 161/162:
Quzzle designed by Jim Lewis circa 2000.
(cardboard box containing plastic tray and 9 plastic pieces, 5.9 x 4.9 x 1/2 inches)
Uses 1x1, 1x2, 2x1, and 2x2 pieces on a 4x5 board like Dad's Puzzle. Below, from the start position shown on the left, slide pieces (without picking them up) to form the end position (a mirror copy of the start position) shown on the right:
It turns out that if the goal is stated to simply to be, from the start position, move the 2x2 to the upper right corner (so it doesn't matter what happens to the other pieces), then a minimal length solution of 93 straight-line moves (equivalent to 84 rectilinear moves) makes a mirror image, and so this simpler problem has the same basic complexity. When it was introduced, Quzzle gained some publicity with claims by the inventor that it requires the largest number of moves for puzzle of its type. There puzzles in Dad's Puzzle family that require many more moves (e.g., Century and a Half requires 169 straight-line moves or 150 rectilinear moves), and even with exactly the same set of pieces as Quzzle, there are puzzles that require more moves. For example, Quzzle Killer of B. Henderson and Gil Dogon (discussed on Pegg's Page and you can play on Baxter's Page) requires more moves just to get the 2x2 piece to the upper right, and 6 additional moves to make the mirror image:
Further Reading
Quirkle Page, from: http://www.quirkle.com
Quzzle Page, from: http://www.quirkle.com/puzzle/index.htm
Quzzle Tips Page, from: http://www.quirkle.com/puzzle/tips.htm
Pegg's Page, from: http://www.maa.org/editorial/mathgames/mathgames_12_13_04.html
Baxter's Page, from: http://www.puzzleworld.org/SlidingBlockPuzzles/qkiller.htm
Here is the solution from the Quzzle Tips Page uses 95 straight-line moves.
Here is a solution of 93 straight-line moves; it corresponds to 84 rectilinear moves (by combining steps 5/6, 14/15, 20/21, 25/26, 34/35, 37/38, 73/74, 79/80, 88/89).
Here is a (minimal) solution of 99 straight-line moves that solve basic Quzzle Killer followed by an additional 6 moves (105 total) to solve the full mirrored version; it cn be converted to 90 rectilinear moves (also known to be minimal) by compining steps 11/12, 20/21, 26/27, 31/32, 40/41, 43/44, 79/80, 85/86, 94/95 for basic Quzzle Killer followed by 6 more moves:
Originally manufactured by Kum-Bak Sports, Toys & Games London, circa 1935;
this puzzle a 1961 Adams Co. Dad's Puzzle,
with cardboard sleeve by J. A. Storer 2007.
(cardboard sleeve, metal tray, and 9 plastic pieces, 3.75 x 3 x 5/16 inches,
the sleeve has directions for Nine Block, Dad's Puzzler, Quzzle, and Quzzle Killer)
The same piece set as Dad's Puzzler, and infact, this name is sometimes used to refer to Dad's Puzzler (e.g., in the Filipiak book). It is presented on the web page of Hirofumi Fujiwara as puzzle 17 of his "Step By Step Problems", and also in the Hordern book.
The start position is different from Dad's Puzzler, but the problem is the same; slide the 2x2 piece from the upper left to the lower left (without picking up pieces):
Here is a solution of 47 straight-line steps; it can be converted to 45 rectilinear moves by combining steps 6/7, 36/37:
(one move = sliding one piece any number of units in one direction)
Like Dad's Puzzler Diagonal, it is natural to consider moving the 2x2 piece to the lower right corner than the lower left:
Like Dad's Puzzler, the diagonal version of Nine Block is an easier problem. Here is a solution of only 29 straight-line moves that can be converted to 27 rectilinear moves by combining steps 6/7 and 18/19:
(with Simple Traffic Jam, Century, and Super Century)
a.k.a. L'Ane Rouge, Which Way Out, Psychotease,
Escaping Jail, Cao Cao Escape, Klotski
Patented in England by J. H. Fleming 1932,
this one is "Which Way Out" by T.C. Timber Brain Twisters circa 1995,
in a box made by J. A. Storer 2007.
(maple, tray and 10 pieces, 2x2 is painted red, 3.75 x 3.5 x 0.9 inches;
box is resized cigar box with brass hardware, 4.75 x 4.75 x 1.75 inches,
lid diagram also shows Simple Traffic Jam, Century, and Super Century)
Hordern's book credits the Red Donkey as the third most sold sliding block puzzle (after the Fifteen puzzle and Dad's Puzzler). It is shown in the 1996 design patent of Mendelsohn and the 200 patent of L. Aryan. The goal is to slide the 2x2 piece (without picking pieces up) to the bottom center so that it can drop out through the opening (we will not charge an extra move for falling through the opening even if the final move of the 2x2 piece is in the horizontal direction). This puzzle is like Simple Traffic Jam, with the 1x2 piece move above the 1x1's. There are a number of starting position variations, the leftmost being the original French L'Ane Rouge:
The September 2000 patent of L. A. Aryan describes the same puzzle as the Red Donkey puzzle. Figure 1 shows the puzzle (the box lid is corrected in a revised Figure 1 at the end of the patent). The claims describe a ten piece sliding piece puzzle with a hinged lid. Some study might be required to determine exactly what is new about this patent. Figure 4 presents a (not minimal) solution of 22 positions that require multiple moves (a total of 99 straight-line moves):
Here is the solution idea that came with Which Way Out. Many of these positions represent several moves (a total of 118 moves straight-line moves):
Here is a solution of 90 straight-line moves for Version A; it can be converted to 81 rectilinear moves by combining steps 10/11, 14/15, 24/25, 39/40, 47/48, 52/53, 55/56, 79/80, and 88/89:
The solution presented on the preceding page for Version A (and also the 81 rectilinear moves solution that is presented in Hordern's book - Puzzle C27d) is minimal and reaches exactly the same position at Step 4 as does a minimal 81 rectilinear moves solution (90 straight-line moves) for the Version B and C start positions (and so step 4 onward can be used for all three puzzles):
The Winning Ways book shows the Version D start position. Step 6 of a minimal solution for this variation is exactly the same as Step 4 above, and so this variation has a minimal solution (for both straight-line and rectilinear moves) of 2 moves longer than Versions A, B, and C (pieces 1, 2, 3, 4 must be renamed to 3, 1, 2, 4):
Simple Traffic Jam
Shafir Games 1981;
minimal solution of 64 rectilinear moves.
Century
Designed by J. H. Conway 1975;
minimal solution of 99 rectilinear moves.
Super Century
Designed by Gil Dogon 2004;
minimal solution of 138 rectilinear moves.
Psychotease, copyright 1969.
(cardboard box and 10 wood pieces, 9 x 11 x 1.5 inches)
Escaping Jail, copyright University Games Co. 1993, made by Raintree Puzzles.
(wood box and 10 wood pieces, 4.4 x 3.25 x 1.2 inches)
Cao Cao Escape, LEO Marketing, 1995
(wood box and 10 wood pieces, 3.8 x 3.125 x 3/4 inches)
Further Reading
Wikipedia Klotski Page, from: http://en.wikipedia.org/wiki/Klotski
Pegg's Page, from: http://www.maa.org/editorial/mathgames/mathgames_12_13_04.html
Baxter's Page,, from: http://www.puzzleworld.org/SlidingBlockPuzzles/4x5.htm
Aryan Patent, from: www.uspto.gov - patent no. 6,116,600
Armendariz Design Patent, from: www.uspto.gov - patent no. 367,502
Mendelsohn Design Patent, from: www.uspto.gov - patent no. 388,840
Shafir Games 1981.
(cardboard cover, plastic tray, and 10 plastic pieces, 4.8 by 4 by 3/8 inches)
Uses 1x1, 1x2, 2x1, and 2x2 pieces on a 4x5 board in the theme of Dad's Puzzler. This puzzle is described in Hordern's book (puzzle C28); it is also shown in Figure 1 of a 1990 patent of T. Monoyios. From the start position shown on the left, slide pieces (without picking them up) to form the end position shown on the right:Here are the directions from the back of the box:
The basic steps for one approach to solve Traffic Jam are shown below, although there are many shorter solutions (the following page shows a minimal length solution).
Here is a solution of 69 straight-line moves; it can be converted to 61 rectilinear moves by combining steps 4/5/6 to 2 moves (rename 243 to 324) and combining steps 2/3, 12/13, 20/21, 26/27, 29/30, 53/54, and 62/63:
(one move = slide one piece any number of units in one direction)
It is natural to consider the simpler puzzle where we only care about the 2x2:
Simple Traffic Jam
It can be that specifying the complete final position can make a big difference; for example, when Century And A Half is changed to just placing the 2x2 piece, only 2/3 as many rectilinear moves are required (the Century puzzle). It is also possible for it to make no difference; for example, when Quzzle is changed to just placing the 2x2 piece, the minimal number of moves does not change. It turns out that the first 64 moves of the Traffic Jam solution of the previous page forms a minimal solution for Simple Traffic Jam, and so only 5 moves are saved. The reverse of the Traffic Jam problem, of course, has the same complexity. But this is not true for the reverse of the simple version:
Reverse Simple Traffic Jam
Here is a 39 straight-line moves solution; it can be converted to to 34 rectilinear moves by combining steps 7/8, 16/17, 25/26, 28/29, 30/31:
Further Reading
Monoyios Patent, from: www.uspto.gov - patent no. 4,927,150
Ling Design Patent, from: www.uspto.gov - patent no. 450,356
Century by J. H. Conway 1975, Super Century by Gil Dogon 2004;
this puzzle formed from two 1961 Adams Co. Dad's Puzzles,
with cardboard sleeve by J. A. Storer 2007.
(cardboard sleeve, metal tray, and 10 plastic pieces, 3.75 x 3 x 5/16 inches)
The goal of both puzzles is to move the 2x2 piece to the bottom center:
Century
designed by J. H. Conway
Super Century
designed by Gil Dogon
Century is discussed in the Winning Ways book (vol. 2) and is shown on the chart on Baxter's Page. It has a minimal soultion of 99 rectilinear moves. The article by E. Pegg gives the following solution summary:
The name of this puzzle comes from the "pure" formulation where the central 1x2 piece is moved to the right by 1/2 unit in the start position. This adds one initial additional move to to make exactly 100 rectilinear moves.
Here is a solution of 111 straight-line moves; it can be converted to to 99 rectilinear moves by combining steps 1/2, 5/6, 17/18, 21/22, 26/27, 30/31, 52/53, 55/56, 59/60, 86/87, 88/89, and 109/110:
(one move = sliding one piece any number of units in one direction)
Super Century is also discussed in the article by E. Pegg, and is also shown in a chart constructed by N. Baxter. Here are positions 0 (the start position), positions10, 20, 30, ..., 140, and position 150 (the end position) of a minimal straight-line solution (the complete solution is shown on the following page):
Here is a solution of 150 straight-line moves; it can be converted to 138 rectilinear moves by combining steps 26/27, 29/30, 53/54, 56/57, 60/61, 70/71, 91/92, 94/95, 98/99, 125/126, 128/128, and 148/149:
(one move = sliding one piece any number of units in one direction)
Further Reading
Pegg's Page, from: http://www.maa.org/editorial/mathgames/mathgames_12_13_04.html
Baxter's Page, from: http://www.puzzleworld.org/SlidingBlockPuzzles/4x5.htm
With Century And A Half and Little House
Made in Asia, purchased 2007.
(felt lined wood tray and 10 wood pieces, 8 by 8.5 by 1 inches)
The directions show Red Donkey (Version C) and a number of other problems. Given the relatively large size of this puzzle, it seemed appropriate to add to these directions two puzzles with long minimal solutions.
Century And A Half
(J. H. Conway, 1978)
Little House
(Pierre-Francois Culand)
The start is the same as the Century puzzle (see Pegg's Page and Baxter's Page), but the goal is a completely specified final position (that is the start position upside-down). The name of this puzzle comes from the "pure" formulation where the central 1x2 piece is moved to the right by 1/2 unit in the start position and moved to the left by 1/2 unit in the end position; this adds two moves to this solution, to make exactly 150 rectilinear moves. Below is a solution of 169 straight-line moves; it can be converted to 148 rectilinear moves by combining the moves 1/2, 5/6, 17/18, 21/22, 30/31, 52/53, 55/56, 59/60, 86/87, 88/89, 107/108, 111/112, 116/117, 118/119, 133/134, 141/142, 145/146, 148/149, 152/153, 164/165, 168/169.
Moves 0 through 79:
(one move = slide one piece any number of units in one direction)
Here is a solution to Little House of 250 straight-line moves, which can be converted to 233 rectilinear moves by combining steps 19/20/21 to 2 steps (and renaming 2,3,4 to be 3,4,2) and combining steps 40/41, 64/65, 74/75, 87/88, 91/92, 94/95, 118/119, 128/129, 134/135, 138/139, 165/166, 189/190, 192/193, 196/197, 208/209, 220/221.
Note that although 250 straight-line moves is minimal, this mechanical conversion to rectilinear moves gives a solution 2 moves greater than the 231 rectilinear move solution indicated on Baxter's Page.
Moves 0 through 71:
(one move = slide one piece any number of units in one direction)
Further Reading
Pegg's Page, from: http://www.maa.org/editorial/mathgames/mathgames_12_13_04.html
Baxter's Page, from: http://www.puzzleworld.org/SlidingBlockPuzzles/4x5.htm
Originally made by Himawari Japan 1981;
this puzzle formed from two 1961 Adams Co. Dad's Puzzles,
with cardboard sleeve by J. A. Storer 2007.
(cardboard sleeve, metal tray, and 10 plastic pieces, 3.75 x 3 x 5/16 inches,
the sleeve has directions for Ushi and Ushi Flipped))
The standard Ushi puzzle is shown on the left and on the right is a common variation where the center portion is flipped:
Ushi
Ushi Flipped
Here is a Ushi solution of 108 straight-line moves; it can be converted to 98 rectilinear moves by combining steps 11/12, 16/17, 20/21, 27/28, 38/39, 50/51, 54/55, 57/58, 81/82, 106/107:
Here is a Ushi Flipped solution of 110 straight-line moves; it can be converted to 103 rectilinear moves by combining steps 28/29, 40/41, 52/53, 56/57, 59/60, 83/84, 108/109:
With Royal Out and King Out
Copyright University Games Co. 1997, made by Sports Pack Puzzles.
(wood box and 11 wood pieces, 4.4 x 3.25 x 1.2 inches)
Here is a solution of 61 straight-line moves; it can be converted to 48 rectilinear moves by combining steps 4/5, 7/8, 14/15, 19/20, 21/22, 25/26, 29/30, 32/33, 36/37, 39/40, 46/47, 50/51, and 59/60:
The Royal Out puzzle is described in Hordern's book as a collection of 5 puzzles consisting of Red Donkey (Version A) and 4 others; of those four, the one shown here requires the greatest number of moves. The King Out puzzle is Hole In One with the bottom row shifted up two units.
Hole In One
Royal Out
King Out
The first 2 straight-line moves of a minimal solution to Royal Out, which can be converted to 1 rectilinear move, yield the start position for Hole In One. Hence, Royal Out Can be solved with 63 straight-line moves, which can be converted to 49 rectilinear moves (by combining steps 1/2 of Royal Out and making the 13 combinations for Hole In One).
Royal Out Minimal Solution First Three Moves
The first 5 straight-line moves of a minimal solution to King Out, which can be converted to 4 rectilinear moves, yield position 15 of Hole In One (the 1x1 pieces can be renamed). Hence King Out can be solved with 51 straight-line moves, which can be converted to 40 rectilinear moves by combining steps 4/5 of King out and steps 19/20, 21/22, 25/26, 29/30, 32/33, 36/37, 39/40, 46/47, 50/51, and 59/60 of Hole In One.
King Out Minimal Solution First Five Moves
Originally manufactured by Hanabishi 1984;
left purchased in Japan 2010, right made by J. A. Storer 2007.
(left: cardboard box, 11 wood pieces + keeper, 4.75" x 5.8" x 7/16";
right: box, 11 purple heart and cherry pieces + keeper, 5" x 6.1" x 1.25")
The object is to move the cow inside the fences:
Here is the solution that was sold with the puzzle:
Here is a solution of 82 straight-line moves; it can be converted to 71 rectilinear moves by combining steps 2/3, 15/16, 19/20, 23/24, 26/27, 30/31, 33/34, 40/41, 45/46, 58/59, and 62/63 (this solution remains minimal even if graphics are ignored, and no solution is possible if the lower right two square are required to be blank):
(one move = sliding one piece any number of units in one direction)
With Fujiwara 15/22/25 and Super Compo
Made by J. A. Storer, 2007.
(wood box with plexiglass bottom, lid, and 13 pieces, 5.75" x 7.75" x 1.25")
A box with a 4x5 tray and a 4x1 side tray to hold unused pieces. There are a total of six 1x1 pieces, six 1x2 pieces, and one 2x2 piece. Many classic 4x5 tray puzzles can be played; Dad's Puzzler, Nine Block, Quzzle / Quzzle Killer, Traffic Jam, Red Donkey, Century, Super Century, Century And A Half, Little House, Ushi, Hole in One, King Out, etc. Hordern's book shows many other puzzles that can be played. Another source for 4x5 tray puzzles is Fujiwara's Step by Step Problems page, which gives 25 problems of increasing difficulty (along with solutions if you get tired). Here are three of them and also Super Compo (designed by Junk Kato - see Baxter's Page), which is similar to but requires more moves that Fujiwara 25:
Fugiwara 15
Fugiwara 22
Fugiwara 25
Super Compo
Further Reading
Fujiwara's Page, from: http://www.pro.or.jp/~fuji/java/puzzle/slide/V1.0/fuji.index-eng.html
Baxter's Page, from: http://www.johnrausch.com/SlidingBlockPuzzles/4x5.htm
Here is a solution of 47 straight-line moves; it can be converted to 43 rectilinear moves by combining steps 13/14, 27/28, 33/34, 45/46:
(one move = sliding one piece any number of units in one direction)
Here is a solution of 64 straight-line moves; it can be converted to 62 rectilinear moves by combining steps 11/12, 53/54:
(one move = sliding one piece any number of units in one direction)
Here is a solution of 111 straight-line moves; it can be converted to 101 rectilinear moves by combining steps 2/3, 19/20, 23/24, 30/31, 41/42, 53/54, 57/58, 60/61, 84/85, 109/110:
(one move = sliding one piece any number of units in one direction)
Here is a solution of 132 straight-line moves; it can be converted to 123 rectilinear moves by combining steps 32/33, 39/40, 42/43, 62/63, 74/75, 78/79, 81/82, 105/106, 130/131:
(one move = sliding one piece any number of units in one direction)
a.k.a. Infants Progress Puzzle
Chad Valley Co. Ltd., Harborne, England, 1920;
made for the Infants Hospital in Vincent Square, London, founded by R. Mond.
(cardboard box, 1/4" thick cardboard tray with 10 pieces, 6.75" x 5+7/8" x 9/16";
instructions on the inside of the box top;
Hordern's book gives the date and a 28 rectilinear /35 straight-line moves solution;
a different puzzle than the Infant's Hospital Puzzle - Dad's Version, and different than the dexterity puzzle A Ward Oin The Infant's Hospital)
Here is a 26 rectilinear moves (32 straight-line moves) solution:
Further Reading
Infants Hospital History, from: http://ezitis.myzen.co.uk/westminsterchildrens.html
Robert Mond Wikipedia Page, from: http://en.wikipedia.org/wiki/Robert_Mond
