MathDB
rectangle with vertices lattice points of saem coloour, red or blue

Source: 2013 Moldova JBMO TST p8

February 25, 2021
Coloringcombinatorial geometrycombinatoricsrectangle

Problem Statement

A point M(x,y)M (x, y) of the Cartesian plane of xOyxOy coordinates is called lattice if it has integer coordinates. Each lattice point is colored red or blue. Prove that in the plan there is at least one rectangle with lattice vertices of the same color.