IMO Shortlist 1998 problem C5


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2. travnja 2012.
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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}}.
Izvor: Međunarodna matematička olimpijada, shortlist 1998