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Mathematics

The Pigeonhole Principle: A Simple Counting Rule with Powerful Consequences

Quick fact

Despite its simplicity, the pigeonhole principle can prove the Erdős–Szekeres theorem: among any sequence of more than (r−1)(s−1) distinct numbers, there is an increasing subsequence of length r or a decreasing subsequence of length s.

Why this is interesting

You have 10 pairs of socks in a drawer, but you can only see the drawer in the dark. How many socks must you pull out to guarantee you have a matching pair?