This tag is for questions involving the Pigeonhole Principle, which roughly states that if $n$ items are placed in $m$ containers and $n>m$, then at least one container has more than one item.

The Pigeonhole Principle roughly states that if $n$ items (e.g. pigeons) are placed in $m$ containers (e.g. pigeonholes) and $n>m,$ then at least one container has more than one item. Stated more formally, the Pigeonhole Principle asserts that there is no injective function whose codomain has smaller cardinality than its domain.

An example application of the Pigeonhole Principle is a demonstration that if five points are placed on a sphere, then there must be some hemisphere which contains at least four of these points: any two points define a great circle, which divides the sphere into two hemispheres. By the Pigeonhole Principle, one of these two hemispheres must contain at least two points. This hemisphere then contains four of the five points (the two on the boundary, and the two found via the Pigeonhole Principle).