MathDB

3

Part of 1934 Eotvos Mathematical Competition

Problems(1)

exist two rectangles in the set such that one contains the other

Source: Eotvos 1934 p3

9/10/2024
We are given an infinite set of rectangles in the plane, each with vertices of the form (0,0)(0, 0), (0,m)(0,m), (n,0)(n, 0) and (n,m) (n,m), where mm and nn are positive integers. Prove that there exist two rectangles in the set such that one contains the other.
combinatoricscombinatorial geometry