rubiks-cube-NxNxN-solver

Overview

This is a rubiks cube solver that can solve any size cube, I have tested up to 17x17x17. The following tables show the reduction in move counts as the solver has evolved. The table starts in July 2018, the earlier releases of the solver had drastically higher move counts, I think it was over 400 moves the first time I solved a 5x5x5.

Solving a 2x2x2 takes around 9 moves while solving a 3x3x3 takes around 20 moves. I am not working on those solvers so I did not include them in the table below.

Move Counts

The move counts here are to reduce the cube to a 3x3x3. Solving the reduced 3x3x3 cube will add another ~20 moves.

| Date | Commit | 4x4x4 | 5x5x5 | 6x6x6 | 7x7x7 | 8x8x8 | 9x9x9 | 10x10x10 | | ------ | ------ | ------ | ------ | ------ | ------ | ------ | ------ | ------ | | 09/28/2021 | 60e964d4| 51.6 | 78.9 | 135.7 | 193.8 | 306.4 | 368.6 | 523.4 | | 09/26/2021 | b6ab34f | 51.6 | 78.9 | 139.7 | 193.8 | 320.6 | 394.4 | 549.2 | | 09/09/2021 | 722673f | 50 | 77.5 | 139 | 193 | 335 | 393 | 573 | | 10/5/2019 | TBD | 50 | 79 | 145 | 202 | 353 | 406 | 618 | | 10/17/2018 | TBD | 50 | 88 | 156 | 218 | 344 | 430 | 601 | | 09/24/2018 | TBD | 50 | 88 | 156 | 218 | 344 | 454 | 630 | | 09/17/2018 | TBD | 50 | 103 | 160 | 221 | 346 | 444 | 614 | | 08/24/2018 | 9dc52a7 | 50 | 103 | 161 | 224 | 346 | 469 | 617 | | 08/20/2018 | 39bf371 | 50 | 103 | 162 | 228 | 366 | 466 | 636 | | 08/19/2018 | 6b8993a | 50 | 103 | 165 | 244 | 362 | 513 | 669 | | 08/13/2018 | b754e60 | 50 | 107 | 165 | 244 | 362 | 513 | 669 | | 08/13/2018 | bdbbd46 | 52 | 107 | 165 | 244 | 362 | 513 | 669 | | 07/16/2018 | 456ddd1 | 52 | 107 | 172 | 247 | 376 | 520 | 725 | | 07/12/2018 | c9484d9 | 60 | 107 | 176 | 247 | 386 | 520 | 743 | | 07/12/2018 | 5cda2c8 | 60 | 107 | 181 | 247 | 386 | 520 | 743 | | 07/08/2018 | 9c13b16 | 60 | 107 | 181 | 257 | 403 | 531 | 743 | | 07/07/2018 | e876493 | 60 | 107 | 181 | 272 | 408 | 556 | 768 | | 07/04/2018 | | 60 | 107 | 200 | 278 | 408 | 556 | 768 |

Install

Install the rubikscubennnsolver python module

bash $ cd ~/ $ git clone https://github.com/dwalton76/rubiks-cube-NxNxN-solver.git $ cd rubiks-cube-NxNxN-solver $ make init

Install 3x3x3 solver

The kociemba solver is required to solve the larger cubes that have been reduced to 3x3x3.

bash $ git clone https://github.com/dwalton76/kociemba.git $ cd ~/kociemba/kociemba/ckociemba/ $ make $ sudo make install

Download lookup tables from Amazon S3 bucket

A few hundred hours of CPU time were used to build the "lookup tables" used by this cube solver. These lookup table are stored in an Amazon S3 bucket and will be downloaded as needed (different size cubes will download different lookup tables). Once downloaded they will not need to be downloaded again.

Usage

Run rubiks-cube-solver.py where --state is your cube state in kociemba order (URFDLB). You must run rubiks-cube-solver.py from the directory that holds your lookup-table*.txt files

Example: bash $ cd ~/rubiks-cube-NxNxN-solver $ source ./venv/bin/activate $ ./rubiks-cube-solver.py --state LFBDUFLDBUBBFDFBLDLFRDFRRURFDFDLULUDLBLUUDRDUDUBBFFRBDFRRRRRRRLFBLLRDLDFBUBLFBLRLURUUBLBDUFUUFBD

History

One of my hobbies is building Lego Mindstorms robots that can solve rubiks cubes. I was able to find solvers for 2x2x2, 3x3x3, 4x4x4 and 5x5x5 but I couldn't find a solver for anything larger than that :( The solvers that I did find for 4x4x4 and 5x5x5 took quite a bit of RAM (several gigs) but I wanted to be able to run the solver on a Lego Mindstorms EV3 which is 300Mhz and 64M of RAM. So I decided to write my own solver and here we are :)

Here is the thread on speedsolving.com where I first posted looking for solvers. I ended up posting updates to this thread as my solver evolved: https://www.speedsolving.com/forum/threads/5x5x5-6x6x6-7x7x7-or-nxnxn-solvers.63592/

Examples

```bash

2x2x2

reset; ./rubiks-cube-solver.py --state DLRRFULLDUBFDURDBFBRBLFU

3x3x3

reset; ./rubiks-cube-solver.py --state RRBBUFBFBRLRRRFRDDURUBFBBRFLUDUDFLLFFLLLLDFBDDDUUBDLUU

4x4x4

reset; ./rubiks-cube-solver.py --state FLDFDLBDFBLFFRRBDRFRRURBRDUBBDLURUDRRBFFBDLUBLUULUFRRFBLDDUULBDBDFLDBLUBFRFUFBDDUBFLLRFLURDULLRU

5x5x5

reset; ./rubiks-cube-solver.py --state LLFBRBFUDULBULBBDDUBBBBLDFDULDLURFBDFRLDUFDBRLDUFBLURFRFRDRBULFBLLLBURUFRFURDDLBULLLRLRDFRDRBBRUDFDUFRBUDULFDUFULDFRBRBULLUFFBLRDDDDFRRBUBRLBUUFFRRDFF

6x6x6

reset; ./rubiks-cube-solver.py --state FBDDDFFUDRFBBLFLLURLDLLUFBLRFDUFLBLLFBFLRRBBFDRRDUBUFRBUBRDLUBFDRLBBRLRUFLBRBDUDFFFDBLUDBBLRDFUUDLBBBRRDRUDLBLDFRUDLLFFUUBFBUUFDLRUDUDBRRBBUFFDRRRDBULRRURULFDBRRULDDRUUULBLLFDFRRFDURFFLDUUBRUFDRFUBLDFULFBFDDUDLBLLRBL

7x7x7

reset; ./rubiks-cube-solver.py --state DBDBDDFBDDLUBDLFRFRBRLLDUFFDUFRBRDFDRUFDFDRDBDBULDBDBDBUFBUFFFULLFLDURRBBRRBRLFUUUDUURBRDUUURFFFLRFLRLDLBUFRLDLDFLLFBDFUFRFFUUUFURDRFULBRFURRBUDDRBDLLRLDLLDLUURFRFBUBURBRUDBDDLRBULBULUBDBBUDRBLFFBLRBURRUFULBRLFDUFDDBULBRLBUFULUDDLLDFRDRDBBFBUBBFLFFRRUFFRLRRDRULLLFRLFULBLLBBBLDFDBRBFDULLULRFDBR

8x8x8

reset; ./rubiks-cube-solver.py --state DRRRURBDDBFBRBDDBRRDUFLLURFBFLFURLFLFRBRFUBDRFDFUUBLFFFUULBBFDBDFBUBBFRFLRDLFDRBBLLFRLDFDRBURULDDRFFBFUUBLLFBRUUFDUBRDBBRDFLURUUFFUDLBRRFDUBFLRUUFFRLBFRFLRULUDFRUBBDBFFLBBDFDFLDBFRRRDDLFLBRBFBBRULDDUUBLBBURULLDDLDRUDRBUDRLUULDURLRDFLFULUFLFULRDDDUBBULRBRDFBBLFURRLULUBDDULRFBRFURBRLBRUBULBDDFBUFFBBRLRUUUFRULLBFFRFDDFFDULLDLBUDLLLLUUBBLDLLBBULULBDUDDFUBFLLDLDLFRDUDDBRRFRURRFRRLDDDDRD

9x9x9

reset; ./rubiks-cube-solver.py --state RFBLRUFLLFFLRRBDUDDBBBDUDFRUDUFFFBBFRBRDURBULFUDDFLLLDLFLRDLDBBBUUBRDBBBDFUFRUURULURBURDLFDUBFFDRDFRUBDUBRFLRRLUDLRLFBLBRRLLRDRBRBLURBLLRFRLDDFFFRBFUFURDFRRUDUFDDRRRLFLLUBBLBFDRRDLBRLUUBRDBBUBFLUUFBLLDBFFFBUFBFDBRDDDFLRFFBFFFLFRRDUUDDBUBLUUDURRBDBFFLFURDDLUBULUULULBFBRUBLLDDFLRBDBRFDUUDFURLLUBUFBLULLURDLLLBLFFRLLBLUDRLRDBLDDBRBUDRBLLRDUUUBRRFBFBBULUDUDLDRFUDDDFULRFRBDUDULBRRDBDFFRUUFRRFBDBLFBBDFURLRFDUUFRLUBURFURDDFLDFUBDFRRURRDLUDRBRBDLBFLBBRDLRDBFDUBDFFUBLFLUULLBUDLLLURDBLFFFDFLF

10x10x10

reset; ./rubiks-cube-solver.py --state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

11x11x11

reset; ./rubiks-cube-solver.py --state URBDLBURUBUFDDRBUFDDUBFRDBLRFUUBLDRLBBUBLUFBLRBFFDDLLLDRULRBUDBBRLULBUUUFFRUBLUFUUBRLBLUUDRLDUBLUFDLBLFDBLFRLFLRUDFLLLDFULDRFDFLLFLLRDUUDRFRFFFFBFRBFRFUUBBUULURLULBBLLDDLBUFRURBLFFBRFFRRURFUFLLRUFDBDDDBLRDUBLBRBLRLBUBULLBBFRBFRBLFUDDULLFBRLDUFBBLDBBFBDBDUFFRRDBUUULDDBRFRDBDDRDRFUDBBFULDLUDBLRRFDBLDBLRFFBDLRBUBLDLUDFUFBDDRUDRDFUBLFFRBDFDDDBULBDRBUDBBDRLUFUFFFFDRBDLRLRDRRBFRLUBFFURFRLRLRRLDBLFLFULBURULDURURBLUFUULFBFULULUDLFLLUFLRFLRLFFDRBLLFRDDDBFBFFBLULDLRUDUURLRUFDRFRDURDUFFFULRRUURUDFURBDLBLLDFBBRDRLUBULFRDLRUFUFDBBDLRRURFULBBBBDBRUDUUULFFBUDLRUBRDDRBFDDBURRLURRDDRRRUURURFUBRRBFRFFFBLBLLDURBDRDFDFRRDRDDLDUFUFFLBDLBBDFLLLFDULDBLDRUUFDURBDLUBBLBDDFFDUURBLDRBRLDBLUDRLRFBFDUFUUBFBRDRFFFFUDDDRFFLDFLRRBLDRRDRFBFBLUDBFBBB

14x14x14

reset; ./rubiks-cube-solver.py --state FBDRLBLRRURRLDRBDLBURDFDDDRBLBBFBRDLLFDUBLFRLDFUUBFRDBFBBBULFRLBUFLBDDDLLDRBFLLBBLFBFFDFBFDDFRRRBDRRBRBDUFDRLRUDLDFDDURFLBUBBUUDLBRRDUDRDBBBLDBRBBBUFLBLRUURBDDLDRLUFFBLFRLDFBRFLDLBULFFBRLDBDDFLLRFLUBFDFBRLRLFDBLBURLBLFRFBLLDULUDURLBUUULLRRLUBDDLURLLRFURFRFRBDDUBLDFBLUDRLRDRRBLFUFRDUFFRULBLRBBRUFDBUBBBBLDBRBLDDRRFDDBFFUUBRBLFUBBRFUURBFDRLURLRBFUUFUBRUDRBDFBBFURFLFFDRDFUFFULFLUBDFUFFDLRRFRUDUDLBBBDLLLDUFUDRFDBLRRFFLRUFDRFURDLRRDRDLFBRLRLULRFBDLFDRLFRDDFLLDBFBUBBRLLDLFURFRFULUBLUBFLFFBFDFBDUUBURUUUBFUBDLLFLUUUFDUDLUUULDLLUDDBUFRDRULRLLULRULFBLUDFURFLFUBDLLFLFUBUUBBUFLUDUBRDBLFFUUUFDRLRULUDDRLRBLRUUFBRRRRULBDLFBFLDLRDFUBLUBRDDFUULFLDLUBFURRURUBDFFFDLRFFLBRFRDRUDUULURULLDFRBUDRDLFUFULDBLUBFRFBURDLLUUFDURLRDBLFFRFDBFURLFUBLUUUFFRULUBURRURFDDBFUFRBURBBDRFUDDFDLRUURFBBDBDRLUBRRBFDFRDFDLRDUFFUBRRBDBBLDLFDUDDRLFRRRBUUUBRFUFBUFFBRRDRDDBBDRUULDRFRFBUFLFFBLRBFLLLRUDFDRUDLDRLFRLUFLUBRDUFDDLLUDDRBUBBBDRDBBFRBDDRRLRRUUBBUDUDBLDBDFLFRFUBFLFDBBLRLULDBRFBRRLUUURDFFFDBLDUDBRFDDFFUBLUUURBBULFUFUDFBRDLLFURBULULBUDLUFFBDRBRRDBUUULFDURRDFDDLUDBDRBFBUFLULURUFDRFRFBBFBBBDRLBLUDLDRDLLDRRLLDLFBRBRLDUFBDDUDBLDFRFBBBDRDRDDLDRULFFLLFLBLDFLURLBUDFBDLRBLFDFLUDDFUBUBLURBBBLFRLFLBDDBURFFBFRRL

15x15x15

reset; ./rubiks-cube-solver.py --state RLURLURBDDULFUUURFLRBLURUBFDBULFLUBBFLDUFBDRFRBRUDFULFRUFLUDFRLFDFLLFDBULURRLBFBUURDULFDFBLRRRLFULLFFFDUULRRRUUUUFDBLDDFFLRDLLUURUBBULUFFURBRRLBBUUBBFDRRBRBRLUDLUDRBFBFULLRRBBFBFRDDDLDDDFRFUFLURUFLBDLUBRLDFRRDBDBFLFUDFLDFFURLFULLDDRURRDLRFLDFLULUUDDRFDRBLRBRBFUFDBDUUDBRRBDFBLBLRBBLBFLLDUBFFFFBDDRLBBBRFDFFUBBDURFLUUDDDRDDLDBRLBULLFLFBRBRBLUDDLRDRDUDFLFRUFLDLBLURDDDRUFDLBRDRLFBDBLDRFBFFBURULUDRRBRDFRFFLULLUBRDRRRDUFRBLFULUBBUFFBRBBFRLFDRRDBLDFRDRDDRLRUULBDURDURFDDLFDUUDBFLBDUFBULFRRDUDUBFBUDBBFUDFUUDLUDDRFDDDFRRRBUDRBFBBULLUFBLRLFLLBRRRRUBDRFLFDFDBLRFLURULULFFBUUUUFDBBLDLUBBRUBBBRBFLULLBLUUULLUBFFDULDFFBFFFUFFDUDRFBUFLDDLURFLRFLRFBUUBLRFDDRULUUUFFRDDBLRDULFURUDDBDLBBUUBFURFRFBRLBUULBLDDDBUBRFFULLUDFFDLDFUBLLBLDFFDDLBDUFUFFLBBBUBULDDFBRRFFLDUDDFRBLRRDDUDLBDBLURBUDBRRLUBBDRFBUFRDRDRBBDULBUFFDRBBDFBUULFFRLLDURRRDFFUUFULDULURLDLUUUDLBBUDLDRFBDBBDLUFBRRFDFLLDLFDBRBBRFUDDDBURDRBUBRUBDUBLDLLDLURLDFDBRUBDLDFRRRBRLULFRFLDRLBUBRUBLFBFDFFLFRFDFLBRULLRBLDRBBFURRRDUUULLULLDLBLBBDFBUUUBRRUFFBRUDBFRDFDLFLFFRFFFFRULDFFDFRUBBBRURBUFLBDFBBBBBRRRLFLFBDRRUFLURDDLRRBRLLFURRURBRFLLLFFURBFULFRFFBLDUUUUBDDUFFDRBRLDDFRBULDDDFFRURUFLDRFLDFBLRUFFUBBDFFDBLLDBDUBDLDLUDFBFLRULRRBDBLRBLDLUURRLLRULDBLBLLRRFDDRBBRBUBDDULDRFBFBBFLUFBLUULDDFDBRLLUBUBBDFBBLBBUBLULDRUDBLRULDUDLUFRRDLLUDDBUFLFLBUFUURFDRDLBURLLRRRULRBFFRRBRFBUBRBUUFRLRDRDLBBRFLLLDDBRFUFRBULFLFDRDDRRDBF ```