Mathologer has a nice video explaining how to solve a cube, and they are really using group theory :), https://youtu.be/-NL76uQOpI0 https://youtu.be/-NL76uQOpI

Mathologer has a nice video explaining how to solve a cube, and they are really using group theory :), https://youtu.be/-NL76uQOpI0 https://youtu.be/-NL76uQOpI0. The key take away is that all you need to do is find a few basic operations (swapping an edge/corner/center) that leaves the rest of the cube unchanged, and then your job is basically done, you apply these until you have a solved cube. This might approach might not give you the optimal algorithm, which has been shown to be able to solve any Rubik's Cube in 20 turns or less [0]. [0] http://www.cube20.org/ http://www.cube20.org/