I was reading the following paper from MIT: http://web.mit.edu/sp.268/www/rubik.pdf
The paper is not difficult to understand, it is more or less a short introduction into group theory, taking the Rubik's Cube as an example of a finite, non-abelian group.
My question: How can I use this fact to find possible ways for solving the cube, if you know what I mean? There are several ways for solving the cube, which seem to me more intuitive rather than a direct result of the group properties.
So if somebody would ask you "It is nice that Rubik's Cube can be seen as an example of a finite group, but what can I do with this knowledge? ", what would you answer?