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RU-SPB 2021 Problem 96

  • Grade 9

A school has 450450 students. Each student has at least 100100 friends among the others and among any 200200 students, there are always two that are friends. Prove that 302302 students can be sent on a kayak trip such that each of the 151151 two seater kayaks contain people who are friends.

D. Karpov

Dataset text AI-MO AoPS. Quoted with source.

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