The PIGEONHOLE PRINCIPLE states that if $n$ pigeons are placed into $m$ holes with $n > m$, then

1. PIGEONHOLE: with more pigeons than holes, by counting, at least ONE hole must contain more than one pigeon. 2. Generalised: if $n$ items go into $m$ boxes, some box has at least $\lceil n/m \rceil$ items. 3. Example: 13 people → at least 2 born in the same month (12 months). 4. Despite its simplicity, pigeonhole proves many surprising results — e.g. any 5 points on a sphere have two within $\pi r$ of each other. 5. Other options are not what the principle states. _Source: Oscar Levin, "Discrete Mathematics: An Open Introduction", §1 (Counting — Pigeonhole referenced)._