Pigeonhole Principle

The pigeonhole principle in mathematics observes that if there are two natural numbers x and y with x > y, then if x items are placed in y categories or pigeonholes, then at least one category or pigeonhole must contain more than one item. This is also known as Dirichlet's box (or drawer) principle.

This principle can be useful to prove apparently difficult problems. For example, this principle can easily prove that at least two people in New Jersey must have precisely the same number of hairs on their head. This is because there are more people living in New Jersey than possible numbers of hairs on one's head.