Pigeonhole principle
Graph theory and combinatorics
If more items are placed into containers than there are containers, then some container holds at least two items.
What is usually left out
The strict inequality does all the work, and no finiteness assumption is needed: if every container held at most one item the placement would be injective, forcing the item count to be at most the container count. Despite being immediate, it is the engine behind a large number of nonconstructive proofs — it shows something exists without indicating where.