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 and average number of moves needed to solve it (if known), and the number of positions.

Regular Permutation Puzzles

Name #Pieces \ Orientation Diameter Avg Depth # 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 26q / 20h 20.67 / 17.70 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
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
CMetrick (1\24)9 15q / ?h 12.254 / ? 8,360,​755,​200
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 16.6962 692,​263,​936
Uriblock 16 ? ? 630,​630,​000
Heptalive 13, 12, 11 26q / 16h 20.147 / 12.119 448,​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 14.156 / 13.290 406,​425,​600
Triplex / Mandorla (full version) 5, 7, 7 33 26.409 381,​024,​000
Dual Circle 6\6, 6\6 36q / 17h 20.678 / 12.992 362,​797,​056
Cohan Circle (1 solution) 19 23q / 17h 18.339 / 12.230 325,​909,​584
Cohan Circle (6 solutions) 19 20q / 14h 16.447 / 10.892 325,​909,​584
Rainbow Cube / Jackpot / 8-colour Dino Star 12 13 9.5518 239,​500,​800
Ultimate Skewb 6\2, 4\3, 4\3 14 10.352 100,​776,​960
Pyraminx 6\2, 4\3, (1\3)8 15 11.7955 75,582,​720
3×3×3 <U,R> group 8\3, 7\1 25q / 20h 19.732 / 15.785 73,483,​200
Puzzler Avenger (colours equivalent) 10, 11 22q / 15h 18.003 / 12.117 52,390,​800
Arusloky (1 solution) 19 22q / 15h 16.657 / 11.223 46,558,​512
Arusloky (2 solutions) 19 20q / 14h 15.763 / 10.556 46,558,​512
Hockey Puck 12 15 11.451 39,916,​800
Rubik's Ufo 12 16q / 14h 12.965 / 11.126 39,916,​800
Ufo (Netblock) 24 16q / 15h 12.060 / 11.150 33,362,​904
Swissmad 12 28q / 21h 18.074 / 14.519 29,937,​600
Dino Cube (6-colour) / Brain Twist / Dino Star 12 11 7.9502 19,958,​400
Dino Cube (6-colour, 2 solutions) 12 10 7.6072 19,958,​400
Twistball Basketball 4+4+4, (1\3)8 ? ? 18,946,​710
Butterfly Puzzle 12, 11 20q / 13h 15.780 / 10.334 14,553,​000
Marusenko Sphere Black and White 4+4, 12+12 ? ? 7,889,​304
Slide Rule Duel Pie 6 12 19q / 11h 14.779 / 8.6679 7,484,​400
Triple Disky 12 15q / 13h 11.005 / 9.9544 7,484,​400
Rashkey 2 10, 10, 7, 6 23q / 19h 17.573 / 14.356 4,961,​250
Halpern Meier Pyramid 6\2, 4\1, (1\3)4 12 8.5081 3,732,​480
2×2×2 8\3 14q / 11h 10.666 / 8.7556 3,674,​160
Rotos (numbered side) 10 19q / 15h 14.206 / 9.5509 3,628,​800
Billiards 9-Ball Puzzle (stationary gap) 10 15 11.697 3,628,​800
Flipside 10 11 8.0429 3,628,​800
Skewb 6\1, 4\3, 4\3 11 8.3636 3,149,​280
Pentahedron 6\1, 6\1, 3\2 13 9.8612 3,110,​400
Super Floppy Cube 4\4 12\1 17q / 15h 12.115 / 9.8558 3,041,​280
Imitation Super Floppy Cube 4\4 12\1 16q / 13h 11.266 / 9.0040 3,041,​280
Puzzler Challenger 10, 11 19q / 13h 14.675 / 9.5556 2,910,​600
Tri-Trick 9 17 12.428 2,903,​040
Diamond Style Puzzler 8, 12 9q, 8h 7.1480 / 6.2089 2,425,​500
Port to Port 18 ? ? 2,056,​320
Gear Mastermorphix 4, (1\24)3, (1\2)3 16q / 10h 10.609 / 7.1446 1,327,​104
Tetraminx 6\2, (1\3)4 11 7.7955 933,​120
Palette Mix 4\10 103q /90h 64.793 / 54.478 720,​000
3×3×3 square group 4, 4, 4, 4, 4 15 10,134 663,​552
Dinomorphix (stickered) 3+3+3+3 10 7.0083 369,​600
Circle Puzzle (1 soln) 3+3+3+3 12q / 12h 8.9442 / 7.5600 369,​600
Circle Puzzle (2 soln) 3+3+3+3 12q / 12h 8.6523 / 7.3238 369,​600
2×3×4 46 14 9.8914 331,​776
Triplex / Mandorla (3-colour) 5, 7, 7 21 16.217 330,​750
2×2×3 Tower Cube 8, 4 15q / 14h 10.603 / 9.7372 241,​920
Gear Cube + 4, (1\24)3 13q / 8h 8.2925 / 5.5263 165,​888
Diamond Skewb 6\2, 4\1 10 6.6921 138,​240
Pyramorphix 4\3 + 4\1 11q / 9h 8.0529 / 6.6337 136,​080
Puzzler Novice 10, 11 18q / 13h 12.533 / 8.3522 97,020
Rashkey 1 10, 10, 7, 6 15q / 12h 11.190 / 9.1118 44,100
Gear Cube 4, (1\12)3 12q / 6h 7.3135 / 4.3032 41,472
Roundy (4 faced) 8\1 9q / 9h 6.6699 / 6.0525 40,320
Slide Rule Duel Pie 3 12 13q / 8h 9.7245 / 5.5990 34,650
Dinomorphix (unstickered) 3+3+3+3 7 4.8448 30,816
Eightball (1 soln) 8 13 9.5196 20,160
Eightball (2 soln) 8 13 9.0299 20,160
Dino Cube (4-colour) 3+3+3+3 7 4.4759 15,408
Palette 7 7 37q 25.469 15,120
Turn'n'Push (<U,R2> group) 6, 5, 2 25q / 20h 16.587 / 14.569 14,400
Columbus Egg 5\10 52q / 15h 27.656 / 8.8512 10,000
Pyraminx Duo (6-colour) 4\3, (1\3)4 7 5.0609 8,748
2-layer Square-1 Star 2+2+2+2+2+2 15q / 10h 10.665 / 6.7520 8,731
Pentaplenty 9, 8 14q / 10h 9.3849 / 6.9182 7,056
Cmetrick Mini 4\24 9q / 8h / ? 6,912
New Seven 7 20 12.069 5,040
Rotos (coloured side) 10 10q / 8h 7.2938 / 4.9905 4,200
Roundy (3 faced) 6\2 9q / 7h 5.4465 / 4.5688 2,880
Saturn 8 9 6.5810 2,520
Beachball Skewb 6, 4 6 4.2694 2,160
Dino Cube (3-colour) 4+4+4 7 5.0014 1,479
1×2×5, Gari Garikun Puzzle 4, 4, 1\2 10 6.1528 1,152
Kép Korong 6\2, 2\2 15q / 14h 10.359 / 9.3576 1,152
Pyraminx Duo 4, 4\3 4 3.0370 324
1×3×3 Floppy Cube 4, 4\2 8 4.4271 192
Rubik's Cheese 6\2 7 4.625 96
Dino Cube (2-colour) 6+6 5 3.25 48
Morph Head 4 3 1.5 6

Bandaged Puzzles

Name #Pieces \ Orientation Max Depth Avg Depth # 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 31f / 13t 25.134 / 10.615 11,​958,​666,​854,​400 / 435,​891,​456,​000
Rotascope 13\3 44q / 36h 32.272 / 27.272 91,082,​880
Slide Rule Duel 6\4, 8\4 22q / 17h 16.470 / 13.156 1,244,​160
Bandaged Cube 8\3, 4\4 35q / 29h 21.938 / 18.801 1,108,​800
Planets 4\24 ? ? 124,​960
Bandaged Pyraminx 4\2, 4\3 13 8.1687 6,912
Nautilus 14 13 5.4969 652
Bandaged 2×2×2 2\2, 4\3 15q / 10h 7.8095 / 5.4167 84

Sliding Puzzles with Gap(s)

Name #Pieces \ Orientation Max Depth Avg Depth # Positions
NHL Hockey Puck Puzzle 69 ? ? 7,​087,​321,​571,​398,​852,​646,​009,​730,​368,​666,​050,​085,​738,​205,​067,​673,​301,​965,​720256,​361,​571,​572,​336,​483,​991,​814,​144,​000,​000,​000,​000,​000
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
Jushbox 27 ? ? 600,​734,​296,​146,​484,​500
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
Orbo / Magic Rainbow Ball 11 34 18.913 479,​001,​600
Bolaris Harmaa 17 ? ? 275,​675,​400
Rack 'em up 16 ? ? 63,​063,​000
Ramka 9 42 26.420 4,​717,​440
Bognar's Brainteaser 4\4, 4\4, 1\4 20 14.140 258,048
Mindlock 11 22 15.032 23,100
Varikon 2 7 19 12.971 20,160
Cubedron 5\4 14 8.3794 15,360
Spongebob 7 25q / 22h 15.180 / 13.276 10,080
Logi Toli 6 19 10.380 4,200
Cybedron (1 soln) 5\4 6 4.3203 256
Cybedron (2 soln) 5\4 6 3.8125 256

Lights Out and other Abelian puzzles

Name # Parts \ States Diameter Avg Depth # Positions
Brainchek PhD 20\6 20 10 109,​684,​753,​201,​889,​280
Rubik's Clock 14\12 12 9.4337 1,283,​918,​464,​548,​864
Lights Out Cube 54\2 29 19.170 281,​474,​976,​710,​656
Brainchek Stoplight 20\3 20 10 104,​603,​532,​030
Lights Out Deluxe 36\2 36 18 68,719,​476,​736
Lights Out 2000 25\3 24 17.113 31,381,​059,​609
Gamze Lights Out (+ move) 25\2 25 12.5 33,554,​432
XL25 Knights Game 25\2 25 12.5 33,554,​432
Brainchek Blinking Eye 20\2 20 10 31,457,​280
Orbik 12\4 23 / 36 / 54 11.605 / 18 / 37.275 16,777,​216
Lights Out (Classic) 25\2 15 9.8998 8,388,​608
Gamze Lights Out (× move) 25\2 16 8.9307 2,097,​152
Gear Shift 4\5, 4\8 4 3.6032 1,280,​000
Lights Out Mini 16\2 16 8 65,536
Orbix (game type 1) 12\2 12 6 4,096
Merlin Magic Square 9\2 9 4.5 512
Writer's Block 7\2 6 3.25 128