14 Sep 2013

APMO 1991 Q2: Upper Secondary Mathematics Competition Question

Suppose there are 997 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 1991 red points in the plane.

Can you find a special case with exactly 1991 red points?


[APMO 1991 Q2]




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