coloring rectangles on the coordinate plane
Source: Estonia IMO TST 2001 p1
March 26, 2020
geometryrectanglecombinatorial geometrycombinatorics
Problem Statement
Consider on the coordinate plane all rectangles whose
(i) vertices have integer coordinates;
(ii) edges are parallel to coordinate axes;
(iii) area is , where
Is it possible to color all points with integer coordinates in two colors so that no such rectangle has all its vertices of the same color?