MathDB

A committee of

3366

film critics are voting for the Oscars. Every critic voted just an actor and just one actress. After the voting, it was found that for every positive integer

n \in \left \{1, 2, \ldots, 100 \right \}

, there is some actor or some actress who was voted exactly

n

times. Prove that there are two critics who voted the same actor and the same actress. (Cyprus)

Problem Statement