One could easily change the puzzle in subtle ways and pose variations of the same question, and one would get vastly different answers depending on the mathematics of the problem. And that is the beauty of it.
Anyway, the question came in in the context of the announcement of a contest for the puzzle in Column 3. We are running a contest for this puzzle in association with the Stanford Math Circle. The problem is really quite a bit easier than it looks. The prize is a $40 Amazon.com gift card. Anybody is eligible to participate but you have to pick up your prize at the Stanford Math Circle meeting. If you are not from the Bay Area, you could use a proxy to pick up the prize. That's about it about the puzzle contest. Happy solving!