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Number of states for twisty puzzles

Chen Shuang edited this page Apr 21, 2024 · 1 revision

Note

  • #states denotes the number of combinations of the puzzle, where permutations within identical pieces (e.g. centers of 4x4x4 cube with same color) are ignored, orientations of face centers are ignored.
  • #states_super denotes the number of combination of the super puzzle, where identical pieces are treated as distinguishable and the orientation of face centers are considered.
  • All puzzle definations are copied from cubing.js, which might be different from normal cognition, e.g. only 180-degree moves are available for pyramorphix.

2x2x2 (c f 0)

  • #states= 3674160
  • #states_super= 3674160

3x3x3 (c f 0.333333333333333)

  • #states= 4.33E+19 = 43252003274489856000
  • #states_super= 8.86E+22 = 88580102706155225088000

4x4x4 (c f 0.5 f 0)

  • #states= 7.4E+45 = 7401196841564901869874093974498574336000000000
  • #states_super= 7.07E+53 = 707195371192426622240452051915172831683411968000000000

5x5x5 (c f 0.6 f 0.2)

  • #states= 2.83E+74 = 282870942277741856536180333107150328293127731985672134721536000000000000000
  • #states_super= 5.29E+93 = 5289239086872492808525454741861751983960246149231077646632506991757159229816832000000000000000

6x6x6 (c f 0.666666666666667 f 0.333333333333333 f 0)

  • #states= 1.57E+116 = 157152858401024063281013959519483771508510790313968742344694684829502629887168573442107637760000000000000000000000000
  • #states_super= 1.31E+148 = 13100024355233283052810092676794378650621714232853978724635727939533635592901050796648498942325745447229267325774462304911360000000000000000000000000

7x7x7 (c f 0.714285714285714 f 0.428571428571429 f 0.142857142857143)

  • #states= 1.95E+160 = 19500551183731307835329126754019748794904992692043434567152132912323232706135469180065278712755853360682328551719137311299993600000000000000000000000000000000000
  • #states_super= 3.04E+211 = 30394959344628313725196721342080594178969399869254568458927606797888466511926167976029813263013109351048271452761427038626673512301072047453583839762885164901951680152889144115200000000000000000000000000000000000

8x8x8 (c f 0.75 f 0.5 f 0.25 f 0)

  • #states= 3.52E+217 = 35173780923109452777509592367006557398539936328978098352427605879843998663990903628634874024098344287402504043608416113016679717941937308041012307368528117622006727311360000000000000000000000000000000000000000000000000
  • #states_super= 2.33E+289 = 23353724131189876512168271318390516987450208930148898921181119386513499225982408507188446113843749245656482211219793230972657112414116278219439446278039837070296161265705342329444852531876787573949274076152634020567414684765443033593576161280000000000000000000000000000000000000000000000000

9x9x9 (c f 0.777777777777778 f 0.555555555555556 f 0.333333333333333 f 0.111111111111111)

  • #states= 1.42E+277 = 14170392390542612915246393916889970752732946384514830589276833655387444667609821068034079045039617216635075219765012566330942990302517903971787699783519265329288048603083134861573075573092224082416866010882486829056000000000000000000000000000000000000000000000000000000000000000
  • #states_super= 1.68E+376 = 16809751140223458272424760501777788523130938093911350611182390070359806658197328025195621690843332309548793029460267557905683379969958528553451303587768715930949136217737613888428518811944806263633543241734427383066486840465994695163996113388364992239184878972888538572079642014954645725674288344275031316525744128000000000000000000000000000000000000000000000000000000000000000

skewb (c v 0)

  • #states= 3149280
  • #states_super= 100776960

master skewb (c v 0.275)

  • #states= 4.22E+28 = 42250536084530912624640000000
  • #states_super= 1.38E+33 = 1384465566417908944884203520000000

professor skewb (c v 0 v 0.38)

  • #states= 3.17E+64 = 31751712428465834357338964143132445189189350195200000000000000000
  • #states_super= 1.09E+75 = 1090980531778059984144992228650164120672646334719001729433600000000000000000

compy cube (c v 0.915641442663986)

  • #states= 5.24E+11 = 523788249600
  • #states_super= 1.45E+10 = 14549673600

helicopter (c e 0.707106781186547)

  • #states= 1.18E+19 = 11848661611315200000
  • #states_super= 1.18E+19 = 11848661611315200000

curvy copter (c e 0.83)

  • #states= 6.32E+19 = 63192861927014400000
  • #states_super= 3.79E+20 = 379157171562086400000

dino (c v 0.577350269189626)

  • #states= 19958400
  • #states_super= 19958400

little chop (c e 0)

  • #states= 1.35E+14 = 135277939046250
  • #states_super= 1.29E+22 = 12926008369442488320000

pyramorphix (t e 0)

  • #states= 24
  • #states_super= 24

mastermorphix (t e 0.346184634065199)

  • #states= 5308416
  • #states_super= 5308416

pyraminx (t v 0.333333333333333 v 1.66666666666667)

  • #states= 75582720
  • #states_super= 75582720

tetraminx (t v 0.333333333333333)

  • #states= 933120
  • #states_super= 933120

master pyraminx (t v 0 v 1 v 2)

  • #states= 2.17E+17 = 217225462874112000
  • #states_super= 5.87E+18 = 5865087497601024000

master tetraminx (t v 0 v 1)

  • #states= 2.68E+15 = 2681795837952000
  • #states_super= 7.24E+16 = 72408487624704000

professor pyraminx (t v -0.2 v 0.6 v 1.4 v 2.2)

  • #states= 1.92E+31 = 19228688422470957567836160000000
  • #states_super= 3.36E+35 = 336425132639551873606861455360000000

professor tetraminx (t v -0.2 v 0.6 v 1.4)

  • #states= 2.37E+29 = 237391215092234044047360000000
  • #states_super= 4.15E+33 = 4153396699253726834652610560000000

royal pyraminx (t v -0.333333333333333 v 0.333333333333333 v 1 v 1.66666666666667 v 2.33333333333333)

  • #states= 5.24E+49 = 52425105093745505455227317179687895040000000000000
  • #states_super= 1.43E+58 = 14264755341376105044291307862676743489511751680000000000000

royal tetraminx (t v -0.333333333333333 v 0.333333333333333 v 1 v 1.66666666666667)

  • #states= 6.47E+47 = 647223519675870437718855767650467840000000000000
  • #states_super= 1.76E+56 = 176108090634272901781374171144157327031009280000000000000

emperor pyraminx (t v -0.428571428571429 v 0.142857142857143 v 0.714285714285714 v 1.28571428571429 v 1.85714285714286 v 2.42857142857143)

  • #states= 2.06E+70 = 20582183665033346731252760185588627707250626464317440000000000000000000
  • #states_super= 6.35E+85 = 63493642565300801642123248005585826168872066473591291524377571491840000000000000000000

emperor tetraminx (t v -0.428571428571429 v 0.142857142857143 v 0.714285714285714 v 1.28571428571429 v 1.85714285714286)

  • #states= 2.54E+68 = 254101032901646255941392101056649724780871931658240000000000000000000
  • #states_super= 7.84E+83 = 783872130435812365952138864266491681097186005846806068202192240640000000000000000000

Jing pyraminx (t f 0)

  • #states= 3732480
  • #states_super= 100776960

master pyramorphix (t e 0.866025403784437)

  • #states= 1327104
  • #states_super= 663552

megaminx (d f 0.7)

  • #states= 1.01E+68 = 100669616553523347122516032313645505168688116411019768627200000000000
  • #states_super= 4.92E+75 = 4915508620777507183716603140314721932064849434131824640000000000000000000000

gigaminx (d f 0.64 f 0.82)

  • #states= 3.65E+263 = 364790115307330759863081610372318101265506588175570326142504636524420418052012591965833824494002983141195363719832622599859321673282378258285548922759556475267223939167970310584246376631322981975599093194264275595527530658078092007833600000000000000000000000000000
  • #states_super= 1.77E+321 = 1769999026971081596626136210218664975727305679442738996896557803120073610269088872616782217187857449900174070287143671828412449753217392042540844562040392079111521059156483175283253597935863183559784599959429918940662260588730578953586271566355097719301734400000000000000000000000000000000000000000000000000000000000000000

pentultimate (d f 0)

  • #states= 5.64E+33 = 5643573414231758192239391539200000
  • #states_super= 1.38E+42 = 1377825540583925339902195200000000000000000

master pentultimate (d f 0.1)

  • #states= 3.75E+131 = 375019654400354707294669633353803254406934223608759102596973605814708295711798760960476283799591402976418152100501913600000000000000
  • #states_super= 4.08E+164 = 408168079675758399486743602420077681306164286932710494706151936097841953549054044822725584360936765008262429021066931129339084800000000000000000000000000000000000000

elite pentultimate (d f 0 f 0.145905)

  • #states= 1.91E+286 = 19085288228427121650439609770193914119589628690030202411929286187060684915502661143430065271127138951944479847678953128405351576427442301665945515719083162855213810611712986863456506119775904690101944001680763368203841916366437706170691711644379056683605148303360000000000000000000000000
  • #states_super= 4.13E+368 = 412832277860719168055227327183855728963127843891619830750034166184725822995600072437273903121095834513265745412404712671205049029008818491369231781086252553896782017229376386575503521502637367962999944984605967262116189091742335504930566257008635158089654200772699405199545083441054227896803000320000000000000000000000000000000000000000000000000000000000000000000000000

starminx (d v 0.937962370425399)

  • #states= 2.48E+50 = 248270459431215031814452911028288348886138880000000
  • #states_super= 8.28E+49 = 82756819810405010604817637009429449628712960000000

starminx 2 (d f 0.23606797749979)

  • #states= 2.65E+104 = 265250107370240367469162414694746375762242569590650060038924753298349372296676352306210867773440000000000
  • #states_super= 2.89E+137 = 288695874172821321990510884511315371379634080616088900725035437706502325786046417604536340030227920977920000000000000000000000000000000000

pyraminx crystal (d f 0.447213595499989)

  • #states= 1.68E+66 = 1677826942558722452041933871894091752811468606850329477120000000000
  • #states_super= 1.68E+66 = 1677826942558722452041933871894091752811468606850329477120000000000

chopasaurus (d v 0)

  • #states= 1.58E+91 = 15800663728104758909644418106446725732410808381024646912387887967512119371614031708160000000
  • #states_super= 3.36E+123 = 3357568651707114723890848010427580505412592679883579924191520615307429180657539536463643803648000000000000000000000000000000

big chop (d e 0)

  • #states= 1.45E+112 = 14516052935043314908425086486921095981497239833952164838015585093892581688832967020876755787637299754488037376000
  • #states_super= 5.77E+161 = 576990221086735801796034753752191543786610230415663802759437338529367082431389144856549058834900528204123296277839635969745972539424768000000000000000000000000000

skewb diamond (o f 0)

  • #states= 138240
  • #states_super= 100776960

FTO (o f 0.333333333333333)

  • #states= 3.14E+22 = 31408133379194880000000
  • #states_super= 1.32E+28 = 13188400838457446891520000000

master FTO (o f 0.5 f 0)

  • #states= 1.48E+44 = 147970626354794338756025552732160000000000000
  • #states_super= 1.71E+59 = 171177064096513260531495694352120921874141020160000000000000

Christopher's jewel (o v 0.577350269189626)

  • #states= 2.01E+15 = 2009078326886400
  • #states_super= 2.01E+15 = 2009078326886400

octastar (o e 0)

  • #states= 1.29E+22 = 12926008369442488320000
  • #states_super= 1.29E+22 = 12926008369442488320000

Trajber's octahedron (o v 0.433012701892219)

  • #states= 4.05E+19 = 40503019070029824000
  • #states_super= 8.86E+22 = 88580102706155225088000

radio chop (i f 0)

  • #states= 9.67E+113 = 967457895180780285952270515975606209946211361882723271959650922368017213678931673088000000000000000000000000000000
  • #states_super= 3.44E+123 = 3439460570041434595205258937511180029934851037929520897952289410802732331405284403206659506176000000000000000000000000000000

icosamate (i v 0)

  • #states= 1.19E+33 = 1185469517577945600000000000000000
  • #states_super= 1.38E+42 = 1377825540583925339902195200000000000000000

icosahedron 2 (i v 0.18759247376021)

  • #states= 1.58E+122 = 157923065373418904957539351074737544630583758186782014483622895529900508388034141319331840000000000000000000000000000000000
  • #states_super= 2.89E+137 = 288695874172821321990510884511315371379634080616088900725035437706502325786046417604536340030227920977920000000000000000000000000000000000

icosahedron 3 (i v 0.18759247376021 e 0)

  • #states= 2.32E+396 = 2316049301420563402622019094121817808649919261027764660300820734666969542073402766657452473402470512752594520726099285052905091451213533402350978624919468419707856115400350205964403580822973895744904033787022439641915310495461602212709310400193009145818552498488482495794930427982355505365839546302316335628655001600000000000000000000000000000000000000000000000000000000000000000000000000000000000
  • #states_super= 1.73E+488 = 172881239502678519142082581583416120426212419814819127630632369008962398056419425288748268528894084185689764583271135856071573284262394490470069249002602083336204358054874042285859400192450895000598622513811914367278747657726849479754550670967748843934214824207021869706602850856045617816972303653386045619350070506186522350722525359804257488182287792403356936279610655403935885889604047626128956419001548800000000000000000000000000000000000000000000000000000000000000000000000000000000000

icosahedron static faces (i v 0.84)

  • #states= 3.48E+48 = 3476722284130350643757822509056000000000000000000
  • #states_super= 6.95E+47 = 695344456826070128751564501811200000000000000000

icosahedron moving faces (i v 0.73)

  • #states= 2.11E+67 = 21146311567333012098028210464258305881119129600000000000000000000000
  • #states_super= 2.46E+76 = 24577543103887535918583015701573609660324247170659123200000000000000000000000

Eitan's star (i f 0.61803398874989)

  • #states= 2.24E+180 = 2244993471433157496895932168123233669700755234365187419849509622026846497302231883092088730046235053190997378990089032638895351209236889600000000000000000000000000000000000000000000
  • #states_super= 1.43E+205 = 14309853539048466370474851248867254196825108194060655872260229418585294590006490724868910777722309004840068133918957864342608932148921181272713242948349392112844800000000000000000000000000000000000000000000

2x2x2 + dino (c f 0 v 0.577350269189626)

  • #states= 2.58E+22 = 25852016738884976640000
  • #states_super= 2.58E+22 = 25852016738884976640000

2x2x2 + little chop (c f 0 e 0)

  • #states= 4.39E+29 = 439202899022422328631337500000
  • #states_super= 8.02E+45 = 8019921233611068269577854211520148275200000000

dino + little chop (c v 0.577350269189626 e 0)

  • #states= 1.35E+14 = 135277939046250
  • #states_super= 1.29E+22 = 12926008369442488320000

2x2x2 + dino + little chop (c f 0 v 0.577350269189626 e 0)

  • #states= 4.39E+29 = 439202899022422328631337500000
  • #states_super= 8.02E+45 = 8019921233611068269577854211520148275200000000

megaminx + chopasaurus (d f 0.61803398875 v 0)

  • #states= 1.58E+91 = 15800663728104758909644418106446725732410808381024646912387887967512119371614031708160000000
  • #states_super= 1.72E+124 = 17197302850207172976026294687555900149674255189647604489761447054013661657026422016033297530880000000000000000000000000000000

starminx combo (d f 0.23606797749979 v 0.937962370425399)

  • #states= 2.65E+104 = 265250107370240367469162414694746375762242569590650060038924753298349372296676352306210867773440000000000
  • #states_super= 2.89E+137 = 288695874172821321990510884511315371379634080616088900725035437706502325786046417604536340030227920977920000000000000000000000000000000000
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