Jaap's Puzzle Page

Puzzle Statistics

On this page I have collected the various statistics of most of the puzzles, namely the number of pieces the puzzle has, the maximum number of moves needed to solve it (if known), and the number of positions.

Regular Permutation Puzzles

Name #Pieces \ Orientation Diameter # Positions
7×7×7 V-Cube 8\3, 12\2, (24\1)8 ? 19,500,551,183, 731,307,835,329,126, 754,019,748,794,904, 992,692,043,434,567, 152,132,912,323,232, 706,135,469,180,065, 278,712,755,853,360, 682,328,551,719,137, 311,299,993,600,000, 000,000,000,000,000, 000,000,000,000,000
6×6×6 V-Cube 8\3, (24\1)6 ? 157,152,858,401, 024,063,281,013,959, 519,483,771,508,510, 790,313,968,742,344, 694,684,829,502,629, 887,168,573,442,107, 637,760,000,000,000, 000,000,000,000,000
Dogic 60\1, 20\3 ? 21,991,107, 793,244,335,592,538, 616,581,443,187,569, 604,232,889,165,919, 156,829,382,848,981, 603,083,878,400,000
5×5×5 Rubik's Cube 8\3, 12\2, (24\1)3 ? 282,870,942,277,741, 856,536,180,333,107, 150,328,293,127,731, 985,672,134,721,536, 000,000,000,000,000
Megaminx 30\2, 20\3 ? 100,669,616, 553,523,347,122,516, 032,313,645,505,168, 688,116,411,019,768, 627,200,000,000,000
Pyraminx Crystal 30\2, 20\3 ? 1,677,826, 942,558,722,452,041, 933,871,894,091,752, 811,468,606,850,329, 477,120,000,000,000
Crazy 4×4×4× II/III 8\3, 8\3, 24\1, 24\1 ? 31,180,187,340,244,394, 380,451,751,732,775, 816,935,095,098,996, 162,560,000,000,000
4×4×6, shape-changing 8\3, (24\1)2, (8\1)3 ? 1,895,062,596,242, 205,714,284,961,357, 866,439,697,401,643, 008,000,000,000,000
Crazy 4×4×4× I 8\3, 8\3, 24\1, 24\1 ? 326,318,176, 648,849,198,250,599, 213,408,124,182,588, 293,120,000,000,000
Chromo Ball / Mystic IQ Ball 30\4 ? 305,815, 726,235,940,368,710, 705,033,637,236,404, 891,156,480,000,000
Mozaika 8\1, 30\4 ? 62,716, 115,731,979,958,427, 000,055,726,386,372, 096,819,200,000,000
4×4×4 Rubik's Cube 8\3, 24\1, 24\1 ? 7,401,196,841,564,901, 869,874,093,974,498, 574,336,000,000,000
Combo Puzzle 36 ? 371,993,326,789, 901,217,467,999,448, 150,835,200,000,000
4×4×6, no shape-changing (8\1)10 ? 18,801,081, 744,320,115,530,520, 330,240,000,000,000
Rainbow Puzzle 40 ? 11,713,322, 080,860,915,346,154, 459,136,000,000,000
Alexander's Star 30\2 ? 72,431, 714,252,715,638,411, 621,302,272,000,000
4×4×6, two-colour, shape-changing 8\3, (24\1)2, (8\1)3 ? 9.6054·1032
4×4×5 88, 4\2 ? 8,881,841,338,019,706, 883,276,800,000,000
Marusenko Sphere with orientations 8\3, 24\1 ? 2,279,626,699,712,199, 018,518,937,600,000
Orbit 56 ? 73,888,773,475,012, 113,089,523,051,000
Master Skewb 24\1, 8\3, 12\1, 6\1 ? 42,250,536,084,530, 912,624,640,000,000
Gear Octahedron 12\6, 6\4, 8\1 ? 10,872,446,393,440, 151,739,039,744,000
Masterball 32 ? 27,360,196,043, 587,190,784,000,000
Impossiball 20\3 ? 23,563,902,142, 421,896,679,424,000
Hungarian Globe 15\8 ? 11,502,425,383, 685,056,364,544,000
Leesho 4 40 ? 7,656,714,453, 153,197,981,835,000
Mad Triad Challenge 36\3 ? 2,670,177,736, 637,149,247,308,800
Square 2 24 1,240,896,803, 466,478,878,720,000
Mad Triad Handy 18\3 ? 826,803,583, 944,627,953,664,000
Rex Skewb 24\1,12\1, 6\1 ? 402,478,052, 931,440,640,000,000
3×4×5, shape-changing 84, 45 ? 41,102,509, 778,424,299,520,000
Face-turning Octahedron 12\1, 6\2, 12, 12 ? 31,408,133, 379,194,880,000,000
Curvy Copter, no jumbling 8\3, (6\1)4, (1\2)12 ? 1,516,628,686,248,345,600,000
Marusenko Sphere Triangular 8, 24 ? 620,590, 250,933,452,800,000
Smart Alex 1\4, 24 ? 605,906, 642,317,616,640,000
Massage Ball 2 30 ? 88,832, 646,059,788,350,720
Hungarian Rings 38 ? 75,406, 424,215,922,599,800
3×3×3 Rubik's Cube 8\3, 12\2 26-29q / 20h 43,252, 003,274,489,856,000
Trajber's Octahedron 8\1, 12\2, (1\4)6 ? 40,503,019,070,029,824,000
Zauberkreuz 20 ? 30,411, 275,102,208,000,000
Octo / Meeting Colors / Disco Puzzle 32 ? 3.7·1018 approx
Equator 15\8 ? 3,120, 232,580,209,704,960
Helicopter Cube, no jumbling 8\3, 6\1, 6\1, 6\1, 6\1 ? 493,694,233,804,800,000
Barrel/Octagon 8\3, 4\1 + 8\2 ? 450,541,700,775,936,000
4×4×6, two-colour, no shape-changing (4+4)10 ? 353,094,061,287,791,616
Topspin 20 ? 121,645,100,408,832,000
Leesho 3 32 ? 99,561,092,450,391,000
3×3×4 8, 8, 8, 8 ? 41,295,442,083,840,000
Astrolabacus 18\2 ? 35,972,733,468,672,000
Gear Cube Extreme + 8, 8\6, 3\2 ? 32,766,669,147,340,800
Siamese Cube 11\2, 6\3, 6\1 ? 14,302,911,135,744,000
Rubik's Fifteen 17 ? 11,381,997,699,072,000
Rubik's Triamid 4\12 + 6\6 ? 4,680,952,735,334,400
Moeraki Nr. 3 48 ? 3,969,069,923,590,200
Octahedron 12\2, 6\4 ? 2,009,078,326,888,000
King Ring / Sando Ring 16, 16 ? 497,117,746,919,592
Rubik's Shells 28 ? 472,518,347,558,400
Gear Cube Extreme 8, 8\3, 3\2 ? 255,989,602,713,600
Marusenko Sphere Classic 2+2+2+2, 6+6+6+6 ? 242,418,070,100,640
Rubik's Rings 34 ? 193,413,243,572,640
Marusenko Sphere Circular 4+4+4+4+4+4 ? 135,277,941,853,080
Gripple 16 ? 20,922,789,888,000
Tricky Disky 16 ? 20,922,789,888,000
It / 4×4 16 ? 10,461,394,944,000
Nintendo Ten Billion Barrel 23 ? 4,509,264,634,875
Starlet / Swesdotchka 45 ? 2,438,362,177,020
3×4×5, no shape-changing (4\1)13 ? 1,981,355,655,168
Brainball 13\2 ? 1,961,990,553,600
Marusenko Sphere Flag 4+4, 4+8+8+4 ? 1,932,542,454,240
Twistball Flower 12, (1\3)8 1,571,364,748,800
SphereXyz 32 ? 337,206,098,790
CMetrick Too 20 ? 305,540,235,000
CMetrick (1\24)9 ? 165,112,971,264
Crazy 2×3×3 (with special move) 8, 8, 8, 7 ? 87,787,929,600
Rashkey 3 10, 10, 7, 6 ? 13,335,840,000
Crazy 2×3×3 8\1, 8\1, 4\2, 3\2 ? 13,005,619,200
Pakoválec 20 ? 12,730,843,125
Super Brain Spinner 20 ? 11,732,745,024
2×3×4, shape-changing, internal bandaging 8, 4\2, (4\1)3, 6 ? 8,360,755,200
Puzzler Avenger / Turnstile 10, 11 ? 6,286,896,000
Triple Cross 18 ? 5,881,075,200
Gerdig Ufo 16 ? 5,108,125,680
2×3×3 Domino with pictures 8, 8, 1\4, 1\4 ? 3,251,404,800
Trillion 17 ? 1,072,071,000
Palette 21 21 ? 1,047,566,520
Crossover 24 32 692,263,936
Uriblock 16 ? 630,630,000
Heptalive 13, 12, 11 26q / 16h 448,493,760
2×3×4, shape-changing, no bandaging 8, 4\2, (4\1)3 ? 418,037,760
2×3×3 Rubik's Domino 8, 8 19q / 18h 406,425,600
Dual Circle 6\6, 6\6 36q / 17h 362,797,056
Cohan Circle (1 solution) 19 23q / 17h 325,909,584
Cohan Circle (6 solutions) 19 20q / 14h 325,909,584
Rainbow Cube / Jackpot / 8-colour Dino Star 12 13 239,500,800
Ufo (Netblock) 24 ? 200,121,075
Ultimate Skewb 6\2, 4\3, 4\3 14 100,776,960
Pyraminx 6\2, 4\3, 4\3 15 75,582,720
3×3×3 <U,R> group 8\3, 7\1 25q / 20h 73,483,200
Arusloky (1 solution) 19 22q / 15h 46,558,512
Arusloky (2 solutions) 19 20q / 14h 46,558,512
Hockey Puck 12 15 39,916,800
Rubik's Ufo 12 16q / 14h 39,916,800
Swissmad 12 28q / 21h 29,937,600
Dino Cube (6-colour) / Brain Twist / Dino Star 12 11 19,958,400
Twistball Basketball 4+4+4, (1\3)8 18,946,710
Butterfly Puzzle 12, 11 20q / 13h 14,553,000
Marusenko Sphere Black and White 4+4, 12+12 ? 7,889,304
Triple Disky 12 15q / 13h 7,484,400
Rashkey 2 10, 10, 7, 6 23q / 19h 4,961,250
Halpern Meier Pyramid 6\2, 4\3, 4\1 12 3,732,480
2×2×2 8\3 14q / 11h 3,674,160
Rotos (numbered side) 10 19q / 15h 3,628,800
Billiards 9-Ball Puzzle (stationary gap) 10 15 3,628,800
Flipside 10 11 3,628,800
Skewb 6\1, 4\3, 4\3 11 3,149,280
Pentahedron 6\1, 6\1, 3\2 13 3,110,400
Super Floppy Cube 4\4 12\1 17q / 15h 3,041,280
Imitation Super Floppy Cube 4\4 12\1 16q / 13h 3,041,280
Puzzler Challenger 10, 11 19q / 13h 2,910,600
Tri-Trick 9 17 2,903,040
Diamond Style Puzzler 8, 12 9 2,425,500
Port to Port 18 ? 2,056,320
Gear Mastermorphix 4, (1\24)3, (1\2)3 16q / 10h 1,327,104
Tetraminx 6\2, 4\3 11 933,120
Palette Mix 4\10 103q /90h 720,000
3×3×3 square group 4, 4, 4, 4, 4 15 663,552
Dinomorphix (stickered) 3+3+3+3 10 369,600
Circle Puzzle 3+3+3+3 12q / 12h 369,600
2×3×4 46 14 331,776
2×2×3 Tower Cube 8, 4 15q / 14h 241,920
Gear Cube + 4, (1\24)3 13q / 8h 165,888
Diamond Skewb 6\2, 4\1 10 138,240
Pyramorphix 4\3 + 4\1 9h 136,080
Puzzler Novice 10, 11 18q / 13h 97,020
Rashkey 1 10, 10, 7, 6 15q / 12h 44,100
Gear Cube 4, (1\12)3 12q / 6h 41,472
Roundy (4 faced) 8\1 9q / 9h 40,320
Dinomorphix (unstickered) 3+3+3+3 7 30,816
Eightball (stationary gap) 8 13 20,160
Dino Cube (4-colour) 3+3+3+3 7 15,408
Palette 7 7 37q 15,120
Turn'n'Push (<U,R2> group) 6, 5, 2 25q / 20h 14,400
Columbus Egg 5\10 52q / 15h 10,000
2-layer Square-1 Star 2+2+2+2+2+2 15q / 10h 8,731
Pentaplenty 9, 8 14q / 10h 7,056
New Seven 7 20 5,040
Rotos (coloured side) 10 10q / 8h 4,200
Roundy (3 faced) 6\2 9q / 7h 2,880
Saturn 8 9 2,520
Beachball Skewb 6, 4 6 2,160
Dino Cube (3-colour) 4+4+4 7 1,479
1×2×5, Gari Garikun Puzzle 4, 4, 1\2 10 1,152
Kép Korong 6\2, 2\2 15q / 14h 1,152
1×3×3 Floppy Cube 4, 4\2 8 192
Rubik's Cheese 6\2 7 96
Dino Cube (2-colour) 6+6 5 48
Morph Head 4 3 6

Bandaged Puzzles

Name #Pieces \ Orientation Diameter # Positions
Ai Cube 8\3, 12\1, 12\1 ? 13,172,009, 005,028,966,400,000
Latch Cube 8\3, 12\2 ? 43,125, 471,270,862,848,000
Battle Gear 15, 14 ? 4,105,946,812,907,520,000
Trio 24 ? 197,480,624,140,800 approx
Square 1 18 ? / 13 435,891,456,000
Rotascope 13\3 44q / 36h 91,082,880
Slide Rule Duel 6\4, 8\4 22q / 17h 1,244,160
Bandaged Cube 8\3, 4\4 35q / 29h 1,108,800
Planets 4\24 ? 124,960
Bandaged Pyraminx 4\2, 4\3 13 6,912
Nautilus 14 13 652
Bandaged 2×2×2 2\2, 4\3 15q / 10h 84

Sliding Puzzles with Gap(s)

Name #Pieces \ Orientation Diameter # Positions
Wisdom Ball 47 ? 1,747,103,301,148,570, 216,747,266,984,449, 397,243,628,503,829, 271,387,695,301,819, 105,280,000,000,000
Saturn (LD Games) 32\2 ? 4,414,602,887,497, 354,033,417,932,709, 098,946,560,000,000
Babylon Tower / Ivory Tower 36 ? 19,116,323,737, 814,368,119,883,304, 974,417,920,000,000
Row by Row 41 ? 28,014,361,976,725,689, 202,886,081,433,600
Back Spin 35 ? 64,084,265,679,291, 581,935,411,200,000
Wanderrings 25 ? 14,363,380,500,124, 493,021,184,000,000
Peter's Black Hole / IQube / Magic Jack 26 ? 5,444,434,725,209, 176,080,384,000,000
Bolaris Maailma 17\4 ? 54,995,971,365,744,175,742,976,000
Delta Ball 19\3 ? 47,127,804,284,843,793,358,848,000
Great Gears 41 ? 145,608, 355,684,298,707,200
Massage Ball 31 ? 61,195, 822,841,187,530,496
Pionir 67 ? 1,662, 357,943,319,673,600
Varikon 3 19 ? 486,580,401,635,328,000
Bolaris Domino 4\1, 13\4 ? 4,933,403,447,132,160
Bolaris Vatavaäri 17 ? 3,201,186,852,864,000
Inversion 19 ? 93,861,960,192,000
Fifteen Puzzle 15 ? 10,461,394,944,000
Clark's Cube 7\24 ? 7,705,271,992,320
Crossteaser / Rolling Cube Puzzle 8\24 ? 270,888,468,480
Missing Link 15 ? 108,972,864,000
Codebreaker 8\4 ? 23,781,703,680
Whip-it 18 ? 571,771,200
Magic Rainbow Ball 11 34 479,001,600
Bolaris Harmaa 17 ? 275,675,400
Rack 'em up 16 ? 63,063,000
Mindlock 11 22 23,100
Varikon 2 7 19 20,160
Cubedron 5\4 14 15,360
Spongebob 7 25q / 22h 10,080
Cybedron 5\4 6 256

Lights Out and other Abelian puzzles

Name # Parts \ States Diameter # Positions
Brainchek PhD 20\6 20 109,684,753,201,889,280
Rubik's Clock 14\12 13 1,283,918,464,548,864
Lights Out Cube 54\2 29 281,474,976,710,656
Brainchek Stoplight 20\3 20 104,603,532,030
Lights Out 2000 25\3 24 31,381,059,609
Brainchek Blinking Eye 20\2 20 31,457,280
Orbik 12\4 23 / 36 / 54 16,777,216
Lights Out (Classic) 25\2 15 8,388,608
Gear Shift 4\5, 4\8 4 1,280,000
Orbix (game type 1) 12\2 12 4,096
Writer's Block 7\2 6 128