# God's algorithm for the <2R, U> subset of the 4x4 cube

Submitted by Ben Whitmore on Wed, 01/24/2018 - 22:00.

Here I'm using sign notation, so 2R is the inner slice only. There are 10 edges, 10 centres in sets of 2, 2, 2 and 4, and 4 permutations of the corner pieces for a total of 4*10!*10!/(2!2!2!4!) = 274,337,280,000 positions. From July 4th 2017 to July 6th 2017, I ran a complete breadth first search of this puzzle in around 60 hours. God's number is 28.

Depth New Total 0 1 1 1 6 7 2 18 25 3 54 79 4 162 241 5 486 727 6 1457 2184 7 4360 6544 8 13048 19592 9 38984 58576 10 116526 175102 11 348180 523282 12 1039946 1563228 13 3103288 4666516 14 9260812 13927328 15 27610283 41537611 16 82268605 123806216 17 244724107 368530323 18 725908778 1094439101 19 2138634030 3233073131 20 6200601206 9433674337 21 17266104701 26699779038 22 43420887999 70120667037 23 84652745882 154773412919 24 90699750007 245473162926 25 28019871154 273493034080 26 843874456 274336908536 27 371461 274337279997 28 3 274337280000 29 0 274337280000The three positions which take 28 moves can be solved with the following algorithms (do the inverse on a solved cube to set up the positions):

U 2R U2 2R U 2R2 U 2R U 2R U' 2R' U 2R2 U2 2R' U 2R' U' 2R' U2 2R U 2R U 2R' U' 2R2 U 2R U 2R U 2R2 U 2R U 2R2 U 2R U 2R U 2R' U2 2R2 U' 2R U 2R' U2 2R' U' 2R' U2 2R' U 2R U 2R' U' 2R' U2 2R' U 2R' U2 2R U 2R2 U 2R U' 2R' U2 2R U2 2R U' 2R2 U2 2R' U2 2R2