rectangles from lattice points
Source: Netherlands - Dutch NMO 1978 p4
January 28, 2023
combinatoricscombinatorial geometrylattice
Problem Statement
On the plane with a rectangular coordinate system, a set of infinitely many rectangles is given. Every rectangle has the origin as one of its vertices. The sides of all rectangles are parallel to the coordinate axes, and all sides have integer lengths. Prove that there are at least two rectangles in the set, one of which completely covers the other.