The story
From the commonly used expository example that if n+1 pigeons are placed in n pigeonholes, at least one pigeonhole must contain two (or more) pigeons.
Etymology from Wiktionary, CC BY-SA 4.0.
pigeonhole principle
Today it means: The theorem which states that any partition of a finite set of n elements into m (< n) subsets (allowing empty subsets) must include a subset with two or more elements; any of certain reformulations concerning the partition of infinite sets where the cardinality of the unpartitioned set exceeds that of the partition (so there is no one-to-one correspondence). Full definition →