Every Rubik's Cube Move Has an Undo — That's Group Theory

[00:00:00]Every move on a Rubik's Cube can be undone. Turn the right face, call it R.

[00:00:04]To reverse it, turn that face the other way. The inverse move is R prime. You are back where you started. R then R prime equals doing nothing. The real power is combining moves. Do R then U.

[00:00:17]Now it is mixed up. To undo a combination, reverse each move and flip the order. U prime then R prime brings it home. The inverse of R U is U prime R prime. Like shoes and socks, last on first off. So, look at what we have.

[00:00:32]Moves combine into moves. Doing nothing is a move, and every move has an inverse. That is the exact definition of a group. Every position you can reach is one element, and there are 43 quintillion of them. Here is the beautiful part. Repeat R then U just 105 times and the cube returns to solved completely on its own. Every move has an inverse. That is group theory.