The Pigeonhole Principle

The Pigeonhole Principle says that if \( n+1 \) or more items are placed into \( n \) boxes, at least one box contains two or more items.

The principle is often used to prove that something must happen or exist.

Examples:

• If $13$ socks are placed into $12$ drawers, at least one drawer has at least $2$ socks.
• In a group of $367$ people, at least two people share the same birthday.

The Pigeonhole Principle is a powerful tool for existence proofs (= proofs that show that something exists.)

Many simple but surprising results follow from this basic idea. See some of them in this article on Medium.com.