Trivially obvious and surprisingly powerful, because it produces existence proofs without construction.
Generalised form: n items in k boxes force some box to hold at least ceiling(n/k).
Interview uses. Any two of thirteen people share a birth month. In any group of six, three are mutual acquaintances or three are mutual strangers. Among any n+1 integers from 1 to 2n, two are coprime and one divides another.
The skill being tested is choosing what plays the role of pigeons and what plays the role of holes - which is rarely obvious and is the whole problem.