16 fun Applications of the Pigeonhole Principle

Mathematical logic can produce some great trivia. Did you know that at every instant, there is a spot in the world where no wind is blowing? It is true, and the proof comes as an application of a fixed point theorem which I discussed a year ago.

This article continues the Thanksgiving tradition of discussing math trivia. These 16 fun tidbits cover topics as disconnected as birthdays, haircuts, WordPress blogs, and cocktail parties. Amazingly, all the results come out of a basic insight from stuffing pigeons into pigeonholes.

The pigeonhole principle

The pigeonhole principle is a powerful tool used in combinatorial math. But the idea is simple and can be explained by the following peculiar problem.

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