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.
2026-04-02 18:26:55.1775154415
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Show me some pigeonhole problems
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The famous Proofs from the book contains a chapter on Pigeon-hole and double counting. You can find there several cute applications of the pigeon-hole principle.
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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.
There are many such problems (with solutions!) in the Math.SE archives. You can try other keywords in the search box at the top right of the page to look for more problems.