[988747]

Somewhat related: I was playing with cube recently, and, starting with solved state, I started doing sequence of two moves that came to my mind: rotate right side down, then the bottom, clockwise. After maybe a 100-150 repetitions (I did not count, just did the moves mindlessly for couple minutes) I went back to solved state. I wonder if there are more such sequences, and how long it takes to go back to original state. The obvious difference from Devil's algorithm was that the 2x2 sub-cube remained untouched the whole time, only the edges were messed up.

[lupire]

Every sequence behaves this way (For all sequences S, there exists n_S such that S ^ n_S equals S^0, the starting state.) Proving this is an introductory problem in Rubik's theory. Try it!

[zeroonetwothree]

Because there are only finitely many states, repeating one move will inevitably get you back to where you started from.

Also check out Lagrange’s theorem in group theory