coloring of lattice points
Source: Simon Marais 2017 B3
April 29, 2021
geometrycombinatoricscombinatorial geometry
Problem Statement
Each point in the plane with integer coordinates is colored red or blue such that the following two properties hold.For any two red points, the line segment joining them does not contain any blue points.
For any two blue points that are distance apart, the midpoint of the line segment joining them is blue.Prove that if three red points are the vertices of a triangle, then the interior of the triangle does not contain any blue points.