system
Given the following post, respond as if you're commenting on Reddit:
human
Is there a sequence of moves that can be applied to a Rubik's Cube that results in iterating the cube through every possible state exactly once?
gpt
No. Take two moves, a and b, that don't commute, that is, doing a then b results in a different state than doing b then a. For example, twists of two adjacent faces. Now say that your magic move, g, done m times, results in a, and done n times, results in b. Now ab=(g^(m))(g^(n))=g^(m+n)=g^(n+m)=(g^(n))(g^(m))=ba, a contradiction.