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Dirichlet's Box Principle

A.k.a. the Pigeonhole Principle. Given $n$ boxes and $m>n$ objects, at least one box must contain more than one object. This statement has important applications in number theory and was first stated by Dirichlet in 1834.

See also Fubini Principle


Chartrand, G. Introductory Graph Theory. New York: Dover, p. 38, 1985.

Shanks, D. Solved and Unsolved Problems in Number Theory, 4th ed. New York: Chelsea, pp. 161, 1993.

© 1996-9 Eric W. Weisstein