Concept
Complementary counting
Counting what is wanted by counting everything and subtracting what is not wanted.
Named by 2 essays across one field — each of them below, with the objects they name alongside 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.
Nobody gets their own hat
Hand back a pile of hats at random and ask for the chance that not one person gets their own. The answer barely moves as the crowd grows — it is a third and a bit at four people, and a third and a bit at four thousand.
Named alongside it
The objects these essays reach for when they reach for this one.
Alternating seriesApproximationBirthday problemCollisionCounting argumentCounting two waysDerangemente, the numberHash collisionIndependencePairsPermutation