Points of a subset with 1788 points are coloured blue
Source: IMO LongList 1988, Netherlands 1, Problem 56 of ILL
November 3, 2005
combinatorics unsolvedcombinatorics
Problem Statement
Given a set of 1988 points in the plane. No four points of the set are collinear. The points of a subset with 1788 points are coloured blue, the remaining 200 are coloured red. Prove that there exists a line in the plane such that each of the two parts into which the line divides the plane contains 894 blue points and 100 red points.