The pigeonhole principle

The pigeonhole principle says that if you place more items than boxes, some box holds at least two items. It sounds obvious and it proves surprising things. Put $10$ pieces on the $8$ files and two must share a file. With $n$ items of $k$ kinds, at least $\lceil n/k \rceil$ share a kind: the largest group cannot be smaller than that ceiling.

The strength is the guarantee. You are not saying this usually happens; you are saying it must, for every arrangement. To use it, name the items and the boxes so the items outnumber the boxes, and the shared box is forced.