Rubik's Cube Orders Table
Here's the idea behind this: starting from the starting sequence, any sequence of moves will eventually bring you back there when performed enough times. The 'order' of a move sequence is the minimal positive integer n such that, starting with a solved cube, performing that move sequence n times will bring you back to the solved state. This page is a table of the shortest known (by me) sequences that have specific orders. A cell is left blank if the shortest sequence is equal to the shortest sequence on a 3x3x3 Cube, or if there is no known sequence (in the case where the 3x3x3 Cube cell is blank).
Before you begin, note that, for any size cube, if X is to turn the top layer on a side, x is to turn the top two layers and cX is to turn the entire cube through that side.
Oh yeah, and if you see these huge numbers and wonder how the hell I had the patience to do that... I didn't. I've got a very nice computer program which does the counting for me, and it's been very useful. If you want it, or have any shorter sequences that you'd like to test out, e-mail me at my e-mail address.
Order |
3x3x3 |
4x4x4 |
5x5x5 |
|---|---|---|---|
| 2 | R² | ||
| 3 | R² U² R² U² cR cU R² U² |
||
| 4 | R | ||
| 5 | R U R' U | ||
| 6 | R² U² | ||
| 7 | F U R U' | ||
| 8 | R L U² | ||
| 9 | cR cU R² F² cR cU R² F² | ||
| 10 | F R U R' F U' R U |
||
| 12 | R² F² U² | ||
| 14 | R U R' D R U R' D | ||
| 15 | R U R² U' F | ||
| 18 | cR cU R² F² | ||
| 20 | R U R' D² | ||
| 24 | r R U | ||
| 28 | R U R' D | ||
| 30 | R U² | ||
| 36 | cU cR F² | ||
| 40 | R² L' F d' | ||
| 42 | r² U | ||
| 45 | R U R D | ||
| 56 | R U R' D L² | ||
| 60 | r U' F | ||
| 63 | R U' | ||
| 70 | r u' r f' | ||
| 72 | cR cU R² F | ||
| 77 | r u r' b | ||
| 84 | F U R | ||
| 88 | cU cR f' u² R² | ||
| 90 | R L U | ||
| 105 | R U | ||
| 120 | r U | ||
| 126 | cR cU R F | ||
| 132 | r u' r' f' u' f² | ||
| 140 | r U' F² | ||
| 144 | f U b' cR | F U² r | |
| 168 | cR f r u² | ||
| 180 | r U' f | ||
| 198 | F u B u R u L u | U r F B d | |
| 210 | cR cU r | ||
| 231 | R U R' U R U L' F' | ||
| 240 | cR cU F | r U | |
| 252 | r U' | ||
| 280 | F b' R l' U d' | ||
| 315 | R B L F | ||
| 330 | f R b D' u' | ||
| 336 | r u² r² f' | f' B cR | |
| 360 | F U R' | ||
| 420 | f u r | ||
| 504 | F u R u B u L | r F cU cR | |
| 560 | r u F | ||
| 630 | cU cR f' U' R' | ||
| 660 | R' B² u L | ||
| 720 | r U' | R f cR cU² l | |
| 780 | F u L u B u R u | ||
| 840 | cR cU' R U² | ||
| 1008 | f u R | ||
| 1260 | cF U | ||
| 1560 | F u B u R u L | ||
| 1680 | R f | ||
| 1980 | U r F B d | ||
| 2310 | f' B² cR cU' | ||
| 2340 | r u' F cU | ||
| 2520 | r F cU | ||
| 2640 | U r F B d² | ||
| 3080 | R L' cR' u | ||
| 3120 | F u B u R u L | ||
| 3276 | f U r d | ||
| 3542 | f R b D² u' | ||
| 3696 | F b R l U | ||
| 3960 | F r' u cU | ||
| 4620 | r U r U L d' | ||
| 5040 | f R b D u | R' f | |
| 8580 | f R b D u' | ||
| 9240 | f R b D u² | ||
| 13860 | R u B cR | ||
| 17160 | f R b D u' | ||
| 17784 | f' B² cR cU² | ||
| 18480 | F b R l U' | ||
| 21840 | R f cR cU² l' | ||
| 25080 | f R u F r U | ||
| 25740 | r u F cU | ||
| 29640 | f' B² cR | ||
| 32760 | f R' b D u² | ||
| 33660 | cU cR f' R | ||
| 47880 | R u B cF | ||
| 51480 | r U r U' L d | ||
| 55440 | F b R l' U | ||
| 60060 | r u F cU r U cU cR | ||
| 65520 | R u' cU | ||
| 90090 | R' L² f cR cU | ||
| 106260 | f R b D² u' | ||
| 203490 | r U cU cR | ||
| 978120 | f' B² cR |