Pigeonhole principle: some applications

De, Prithwijit (2018) Pigeonhole principle: some applications. At Right Angles, 7 (3). pp. 74-78. ISSN 2582-1873

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Abstract

The Pigeonhole Principle (PHP) or the Dirichlet Principle is perhaps the easiest theorem that exists in all of Mathematics. It states that if n + 1 pigeons are put into n pigeonholes, then there is at least one pigeonhole with more than one pigeon. The proof is as easy as the statement. Assume the contrary. Then every pigeonhole has at most one pigeon and therefore the total number of pigeons is at most n. A contradiction. It is natural to ask what is so special about something so trivial. The answer lies in the applications. The goal of this article is to serve up a delectable collection of examples of applications of PHP to the reader.

Item Type:	Articles in APF Magazines
Authors:	De, Prithwijit
Document Language:	Language English
Uncontrolled Keywords:	Pigeonhole, Principle, Pigeons
Subjects:	Natural Sciences > Mathematics
Divisions:	Azim Premji University - Bengaluru > University Publications > At Right Angles
Full Text Status:	Public
URI:	http://publications.azimpremjiuniversity.edu.in/id/eprint/1786
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