# What is God's Number for the Rubik's Picture Cube?

It's been well known for a few years now that every Rubik's Cube scramble can be solved in 20 moves.

However, this is only for the case where the orientation of the centers is not taken into consideration. I couldn't find a reference for the picture cube, where face orientation does matter. Does anybody know a resource on the minimum number of moves required to solve a picture cube?

• Not a complete answer, but even on a standard rubiks cube, the sides and corners must be in exactly the correct position and orientation. The only difference is that each of the centers may be rotated to one of four orientations. Hopefully that is a start for those who write an answer. Jan 24 '15 at 5:59
• I think a counting argument gives a lower bound of 22. For a trivial upper bound, is there a short sequence to rotate a single center cube or multiple of them?
– xnor
Jan 24 '15 at 9:45
• @xnor: Could you expand on your counting argument? It's not obvious to me. Jan 24 '15 at 13:55
• @xnor Counting only gives you 21. Jan 24 '15 at 22:00
• By "minimum," do you mean "maximum" or "least upper bound"? The minimum number of moves required to solve a cube is $0$, which occurs when every piece is already in the correct position. Jan 26 '15 at 19:34