A lattice point is a point that has integer coordinates
MATHEMATICS · Subjective · AoPS · Mathematics · Follow the Rules · Follow the Rules
Problem
A lattice point is a point that has integer coordinates. Suppose each lattice point in the cartesian plane is colored either red or blue. Let R be a 2×6 rectangle whose sides are parallel to the axes and corners are lattice points. (That is R contains three lattice points on one side and seven on the other). A monochromatic rectangle is a rectangle whose sides are parallel to the axes and whose four corners are lattice points having same color. Prove that R must contain a monochromatic rectangle.