By this I mean books with math puzzles and problems similar to the ones you would find in mathematical olympiads.
- Anybody can ask a question
- Anybody can answer
- The best answers are voted up and rise to the top
If you're after Olympiad-level books, get The IMO Compendium which is a collection of problems from the International Math Olympiad, 1959-2004. You can find similar books with national Olympiad problems by going to Amazon and searching for "mathematical Olympiad".
There are lots of other books with similar titles and descriptions. Just follow Google Books's suggestions.
Art of Problem Solving: http://www.artofproblemsolving.com/Store/index.php
Anything by Martin Gardner.
THE PENGUIN DICTIONARY OF CURIOUS AND INTERESTING NUMBERS, by David Wells.
Sample entry: $199: 199 + 210n$ for $n = 0, 1, 2, 3, 4, 5, 6, 7, 8, 9$ provides the smallest $8, 9$ and $10$ primes in arithmetical progression.
Obviously you can reformulate any of the information given in the book as a problem to pose to someone else.