Školjka

%V0 In the Cartesian coordinate plane define the strips $S_n = \{(x,y)|n\le x < n + 1\}$, $n\in\mathbb{Z}$ and color each strip black or white. Prove that any rectangle which is not a square can be placed in the plane so that its vertices have the same color. IMO Shortlist 2007 Problem C5 as it appears in the official booklet:In the Cartesian coordinate plane define the strips $S_n = \{(x,y)|n\le x < n + 1\}$ for every integer $n.$ Assume each strip $S_n$ is colored either red or blue, and let $a$ and $b$ be two distinct positive integers. Prove that there exists a rectangle with side length $a$ and $b$ such that its vertices have the same color. Edited by Orlando Döhring Author: Radu Gologan and Dan Schwarz, Romania