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RU-SPB 2009 Problem 92

  • Grade 9

There are 4040 members of jury, that want to choose problem for contest. There are list with 3030 problems. They want to find such problem, that can be solved at least half members , but not all. Every member solved 2626 problems, and every two members solved different sets of problems. Prove, that they can find problem for contest.

Dataset text AI-MO AoPS. Quoted with source.

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