Problem #PRU-79384

Problems Combinatorics Integer lattices Integer lattices (other) Methods Pigeonhole principle Pigeonhole principle (finite number of poits, lines etc.)

Problem

There are several squares on a rectangular sheet of chequered paper of size \(m \times n\) cells, the sides of which run along the vertical and horizontal lines of the paper. It is known that no two squares coincide and no square contains another square within itself. What is the largest number of such squares?