KURSCHAK 1970 Problem 3
n points are taken in the plane, no three collinear. Some of the line segments between the points are painted red and some are painted blue, so that between any two points there is a unique path along colored edges. Show that the uncolored edges can be painted (each edge either red or blue) so that all triangles have an odd number of red sides.
Dataset text AI-MO AoPS. Quoted with source.
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