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

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              274337280000```
The 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```