IMO 2007 Shortlist C5
In the Cartesian coordinate plane define the strip Sn = {(x,y) | n ≤ x < n + 1} for every integer n. Assume that each st...
Category: Combinatorics
Problem
In the Cartesian coordinate plane define the strip Sn = {(x,y) | n ≤ x < n + 1} for every integer n. Assume that each strip Sn is colored either red or blue, and let a and b be two distinct positive integers. Prove that there exists a rectangle with side lengths a and b such that its vertices have the same color. (Romania)