Dear Mods: this may be a non-research question, but I am asking it because from my knowledge, the question appears nontrivial.
This video claims that a Rubik's cube can be "solved" from any starting position with the repeated application of two fixed moves. The method is easily seen as wrong because the specific moves he suggests actually leave the bottom right $2\times 2 \times 3$ block unaffected. My question is more general: does there exist a finite set of moves which if applied repeatedly from any starting position, yield a solved Rubik's cube?
Moves can be thought of as permutations on the set configurations of a Rubik's cube. A solved Rubik's cube is a specific configuration of interest. If these moves get you from any configuration to a solved configuration, then (by symmetry) these moves must get you from any configuration to any other configuration. This means these moves constitute a permutation of maximum period. Does such a permutation even exist? What is known about the existence of such a permutation?