Roy Johnson,
I had discussed this problem along with my own meditation Arbitrarily Nested Loops with several monks, so don't feel bad about having an advantage. I do not know for a fact, my solution is correct since some of the shortcuts I took may be invalid. Since the answer itself doesn't have any tangible real-world value, I am interested in any and all responses. Some of the more astute mathematically inclined monks may come up with an answer without any code at all - that's fine too.