It's pretty simple to see that you can reach any possible configuration of a Rubik's cube (check Wikipedia if you're not sure what that is!) with just six basis operations. Namely, a counterclockwise quarter rotation around each of the axes: +x,-x,+y,-y,+z,-z.

But perhaps all six operations aren't necessary, so that it is possible to reach the same configuration following from a turn around +x by some combination of turns around the other five faces?

Explain why rotations around all six faces are independent or, alternatively, come up with a sequence of rotations about -x,+y,-y,+z,-z which mimic the effect of a rotation about +x.

Consider relationships between some subset of cuboids which remain invariant under some, but not all, of the six basic operators.

Posted by FrankM on 2019-05-27 12:56:09