Today, I got the following message:

Hi Ed! I think you'd like this colorful puzzle: http://www.alientiles.com
Dr. Cliff Pickover

The game described here is an easy way to introduce groups to people. Is
there an easy way to determine the number of disjoint sets there are in this
structure? The page shows an 8x8 square with 4 colors. Is there a formula
that gives the number of disjoint sets of a nxn square of k colors?

--Ed Pegg Jr, www.mathpuzzle.com