This website contains problems from math contests. Problems and corresponding tags were obtained from the Art of Problem Solving website.

Tags were heavily modified to better represent problems.

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Found problems: 1

2015 District Olympiad, 2
Tags: discrete math , real life problem
At a math contest there were $ 50 $ participants, where they were given $ 3 $ problems each to solve. The results have shown that every candidate has solved correctly at least one problem, and that a total of $ 100 $ problems have been evaluated by the jury as correct. Show that there were, at most, $ 25 $ winners who got the maximum score.