Pigeonhole principle An image of pigeons in holes. Here there are n = 10 pigeons in m = 9 holes. Since 10 is greater than 9, the pigeonhole principle says that at least one hole has more than one pigeon. In mathematics, the pigeonhole principle states that if n items are put into m containers, with n &gt; m , then at least one container must contain more than one item. This theorem is exemplified in real-life by truisms like "there must be at least two left gloves or two right gloves in a group of three gloves". It is an example of a counting argument , and despite seeming intuitive it can be used to demonstrate possibly unexpected results; for example, that two people in London have the same number of hairs on their heads (see below ). The first formalization of the idea is believed to have been made by Peter Gustav Lejeune Dirichlet in 1834 under the name Schubfachprinzip ("drawer principle" or "shelf principle"). For this reason it is also commonly called Dirichlet's box principle , Dirichlet's drawer principle or simply "Dirichlet principle" — a name that could also refer to the minimum principle for harmonic functions . The original "drawer" name is still in use in French ("principe des tiroirs"), Polish ("zasada szufladkowa"), Hungarian ("skatulyaelv"), Italian ("principio dei cassetti"), German ("Schubfachprinzip"), Danish ("Skuffeprincippet"), and Chinese ("抽屉原理"). Imagine five people who want to play softball ( n = 5 items), with a limitation of only four softball