Over at Good Math, Bad Math, MarkCC has a nice post introducing groupoids which uses the fifteen puzzle as an example. I like this example a lot, and I thought it would be interesting to expand on it a bit. So I’m going to tell you:

- Why the Rubik’s Cube is a finite group,
- Why the fifteen puzzle is a finite groupoid, and
- How to solve the fifteen puzzle.

I’m not going to assume any knowledge of groups or groupoids, but if you don’t know much group theory, you’ll have to skip over certain parts of the second half.