De, Prithwijit
(2018)
Pigeonhole principle: some applications.
At Right Angles, 7 (3).
pp. 7478.
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.
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