The Pigeonhole Principle

Too many pigeons

An interactive lesson with 6 steps, about 5 minutes: you predict, drag and solve, with instant feedback on every answer. It runs in your browser and needs JavaScript.

What you’ll learn

• n + 1 pigeons in n holes means some hole has at least 2.
• More generally, kn + 1 pigeons guarantee some hole has at least k + 1.
• The trick is choosing what counts as the “pigeons” and the “holes”.

Steps

1. Socks in the dark
2. The principle
3. Hairy heads
4. Birthday months
5. The worst case
6. Handshakes