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TOT 279 1990 Autumn A S4 10 red and 10 white points

Source:

June 8, 2024
geometrycombinatoricscombinatorial geometry

Problem Statement

There are 2020 points in the plane and no three of them are collinear. Of these points 1010 are red while the other 1010 are blue. Prove that there exists a straight line such that there are 55 red points and 55 blue points on either side of this line.
(A Kushnirenko, Moscow)
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