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1991 APMO Problems/Problem 2

Revision as of 00:48, 9 November 2025 by Maphycom (talk | contribs) (→Problem)

Problem

Suppose there are $997$ points given in a plane. If every two points are joined by a line segment with its midpoint colored in red, show that there are at least $1991$ red points in the plane. Can you find a special case with exactly $1991$ red points?

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