Deven Gill : Some interesting pigeon hole problems

Posted by Josh Fletcher , part of the MATH Club.

At

Nov. 6, 2023, 1 p.m.

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636 SEO

Abstract

The pigeon principle is a fundamental concept in combinatorics. Its applications are wide-reaching, extending well beyond the scope of combinatorics alone. The principle is summarized as follows: Given n+1 balls which we must distribute into n urns, there is at least one urn with two or more balls. A more general form states the following: Given n balls and k urns then there is at least one urn with at least ceiling(n/k) balls. We'll look at a few applications of this principle to problems appearing in competition mathematics, number theory, and geometry. By the end of this talk, you should have acquired a sense of the pigeonhole principle's importance and utility.

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