Ooooh, Sexy

Geometry Level 4

When solving a Rubik's Cube, a common algorithm in speedcubing is the "sexy move," in which the solver performs the moveset \(R\) \(U\) \(R'\) \(U',\) meaning, "rotate the rightmost face \(90^{\circ}\) clockwise, then the uppermost face \(90^{\circ}\) clockwise, then the rightmost face \(90^{\circ}\) counterclockwise, then the uppermost face \(90^{\circ}\) counterclockwise."

How many times will a solver have to perform the "sexy move," starting in a solved state, before he returns to the solved state again?

Learn more about Rubik's move notation here.

A nod to Josh Silverman for precedence.

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