The Pigeonhole principle

Thinking mathematically, Part A

The pigeonhole principle is a simple, yet beautiful and useful idea. Given a set A of pigeons and a set B of pigeonholes, if all the pigeons fly into a pigeonhole and there are more pigeons than holes, then one of the pigeonholes has to contain more than one pigeon.

The pigeonhole principle states that if n items are put into m containers, with n > m, then at least one container must contain more than one item.

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