IMO Shortlist 1998 problem C5
Dodao/la:
arhiva2. travnja 2012. In a contest, there are

candidates and

judges, where

is an odd integer. Each candidate is evaluated by each judge as either pass or fail. Suppose that each pair of judges agrees on at most

candidates. Prove that
%V0
In a contest, there are $m$ candidates and $n$ judges, where $n\geq 3$ is an odd integer. Each candidate is evaluated by each judge as either pass or fail. Suppose that each pair of judges agrees on at most $k$ candidates. Prove that $${\frac{k}{m}} \geq {\frac{n-1}{2n}}.$$
Izvor: Međunarodna matematička olimpijada, shortlist 1998