Get a Rubik's cube and determine the order of the move "rotate top face a quarter-turn clockwise and then the right face a quarter-turn away from you." That is, how many iterations of this move will return a clean cube to a clean cube again? Write this move out as a permutation of the pieces in a Rubik's cube and then find its order using the disjoint cycle decomposition of that permutation.
I used the Rubik's Cube, and found the answer to be 63. However, I am unsure as to how to write the move as a permutation of the pieces and using cycle decomposition to find it's order.