Thanks for your quick response! I have to admit I'm more than a bit embarrassed that I didn't use modulo arithmetic. For some reason when I thought of the idea, I didn't think it would help me any .. but that kind of problem is precisely what modulo arithmetic is suited for. Perhaps you could leave my name off the problem if you post it, since I feel not so proud of my question; although I think the problem as a whole is a good one.

I really think you are providing an excellent educational service. Thanks again.

Sincerely,
Brad

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