101 blue and 101 red points are selected on the plane, no 3 on straight line
Source: 2016 Kazakhstan MO grades XI P5
November 2, 2020
combinatoricsColoringpointscombinatorial geometry
Problem Statement
blue and red points are selected on the plane, and no three lie on one straight line. The sum of the pairwise distances between the red points is (that is, the sum of the lengths of the segments with ends at red points), the sum of the pairwise distances between the blue ones is also , and the sum of the lengths of the segments with the ends of different colors is . Prove that you can draw a straight line separating everything red dots from all blue ones.