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“Commutators” is a term used for a class of moves used to change the orentation or position of just two or three pieces, while leaving the rest of the cube undisturbed.
Also, HE’s currently trying to solve a 200x200x200 supercube that’s in the TARDIS’s game room. Simple 3x3x3s like the classic Rubik’s cube are a piece of cake for him.
Also, I do believe “permutations” would make a whole lot more sense than “commutators” in that sentence.