Concept
Collision
Two things landing in the same place, which is what a counting argument produces when there are more things than places.
Named by 2 essays across 2 fields — each of them below, with the objects they name alongside it.
More things than boxes
If there are more objects than containers, some container holds two. That is the entire principle, it is impossible to disagree with, and it settles questions that look nothing like it.
Twenty-three people
A room needs 253 people before someone probably shares a birthday with you. It needs 23 before two of them probably share one with each other. The gap between those numbers is the whole problem.
Named alongside it
The objects these essays reach for when they reach for this one.
Birthday problemComplementary countingCounting argumentDirichletExistence proofHash collisionIndependenceNonconstructivePairsPigeonhole principle