Re: interesting math problem
The USSR Olympiad Problem Book is published by Dover Publications. I love Dover. I'm sure you can get it off Amazon. It has solutions to every problem in the book, as well. If you don't want to spend $15 or so on that, try Googling for USAMO, Soviet Olympiad or Putnam problems. Putnam problems are generally beastly, so they wouldn't be my starting point.
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