even number of points in a plane, half red half blue
Source: Netherlands - Dutch NMO 1977 p4
January 28, 2023
geometrycombinatoricscombinatorial geometry
Problem Statement
There are an even number of points in a plane. No three of them lie on one straight line. Half of the points are red, the other half are blue. Prove that there exists a connecting line of a red and a blue point such that in each of the half-planes bounded by that line the number of red points is equal to the number of blue points.