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Colouring points

Source: APMO 1991

March 11, 2006
inductiongeometryparallelogramanalytic geometrycombinatorial geometrycombinatorics unsolvedcombinatorics

Problem Statement

Suppose there are 997997 points given in a plane. If every two points are joined by a line segment with its midpoint coloured in red, show that there are at least 19911991 red points in the plane. Can you find a special case with exactly 19911991 red points?
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