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
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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 $${\frac{k}{m}} \geq {\frac{n-1}{2n}}.$$
Školjka