101 brown points, 101 green points, equal sums of 1-coloured segments
Source: Ukrainian Geometry Olympiad 2020, X p5 , XI p4
April 27, 2020
Coloringcombinatoricscombinatorial geometrygeometrypoints
Problem Statement
On the plane painted points in brown and another points in green so that there are no three lying on one line. It turns out that the sum of the lengths of all segments with brown ends equals the length of all segments with green ends equal to , and the sum of the lengths of all segments with multicolored equals . Prove that it is possible to draw a straight line so that all brown points are on one side relative to it and all green points are on the other.