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.

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Posted by tonny ken on 2019-10-04 01:55:12