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BG-MO 1985 Problem 4

    Seven points are given in space, no four of which are on a plane. Each of the segments with the endpoints in these points is painted black or red. Prove that there are two monochromatic triangles (not necessarily both of the same color) with no common edge. Does the statement hold for six points?

    Dataset text AI-MO AoPS. Quoted with source.

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