Show that we can find three points of the same color
Source: Canada National Mathematical Olympiad 1988 - Problem 3
October 3, 2011
combinatorics proposedcombinatorics
Problem Statement
Suppose that is a finite set of at least five points in the plane; some are coloured red, the others are coloured blue. No subset of three or more similarly coloured points is collinear. Show that there is a triangle
(i) whose vertices are all the same colour, and
(ii) at least one side of the triangle does not contain a point of the opposite colour.