Abstract
If many pigeons roost in few pigeonholes then there must be a hole with many pigeons. This is so obvious that you may be surprised how many mathematical arguments are based on such reasoning, and what surprising consequences it has. It is an important tool for proofs of existence. The art is in recognising when and how it can be used. This is sometimes quite obvious, but sometimes hard to discern.
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Grieser, D. (2018). The pigeonhole principle. In: Exploring Mathematics. Springer Undergraduate Mathematics Series. Springer, Cham. https://doi.org/10.1007/978-3-319-90321-7_9
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DOI: https://doi.org/10.1007/978-3-319-90321-7_9
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Online ISBN: 978-3-319-90321-7
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