cuBerBruce
Member
I've done an analysis of the optimal number of moves (face turns) to solve each case of the supercube cross. By supercube cross, I mean solving the 4 cross edges and orienting the 5 centers adjacent to those edge positions. This is for solving a particular color cross. (It's not for color neutral solving.) The distribution is:
The 6 antipodes include two equivalence classes. Scrambles to generate cases of these two equivalence classes are:
L2 F' R B2 U F2 R B' D B' F' D'
F R B2 U2 L' D' F' D2 L F2 R' D'
(EDIT: The above are for generating antipode cases for the D cross.)
The average number of moves for solving a particular color cross is approximately 8.7636.
Code:
moves positions
----- ---------
0 1
1 15
2 158
3 1682
4 17469
5 166685
6 1425198
7 10144474
8 49800450
9 104027538
10 28994240
11 64004
12 6
---------
total 194641920
The 6 antipodes include two equivalence classes. Scrambles to generate cases of these two equivalence classes are:
L2 F' R B2 U F2 R B' D B' F' D'
F R B2 U2 L' D' F' D2 L F2 R' D'
(EDIT: The above are for generating antipode cases for the D cross.)
The average number of moves for solving a particular color cross is approximately 8.7636.
Last edited: