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CMO 1976 Problem 8

  • Paper

Each of the 36 line segments joining 9 distinct points on a circle is coloured either red or blue. Suppose that each triangle determined by 3 of the 9 points contains at least one red side. Prove that there are four points such that the 6 segments connecting them are all red.

Dataset text AI-MO AoPS. Quoted with source.

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