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KöMaL problem A, 2026

Combinatorics Difficulty 6.0 National Olympiad Prove it Hungary

20262026 people visited an exhibition where 10001000 paintings were displayed. Prove that it is possible to send some of the visitors to two rooms, with at least one visitor in each room, such that there is no painting that was liked by someone in one room but by nobody in the other, and there is no painting whose painter is personally known by someone in one room but by nobody in the other.

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