TITLE: Which books would you recommend about Recreational Mathematics?
QUESTION [14 upvotes]: By this I mean books  with math puzzles and problems similar to the ones you would find in mathematical olympiads.

REPLY [3 votes]: 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.