MathDB

3

Part of 2015 Balkan MO

Problems(1)

BMO 2015 #3: Oscars

Source: BMO 2015 problem 3

5/5/2015
A committee of 33663366 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∈{1,2,…,100}n \in \left \{1, 2, \ldots, 100 \right \}, there is some actor or some actress who was voted exactly nn times. Prove that there are two critics who voted the same actor and the same actress. (Cyprus)