Show me some pigeonhole problems I'm preparing myself to a combinatorics test. A part of it will concentrate on the pigeonhole principle. Thus, I need some hard to very hard problems in the subject to solve.
I would be thankful if you can send me links\books\or just a lone problem.

This turned up in a routine google search of the phrase "pidgeonhole principle exercise" and appears to be training problems for the New Zealand olympiad team. It contains numerous problems and has some solutions in the back.
