lattice set of squares, friendly sets
Source: 2014 Austrian Federal Competition For Advanced Students, Part 1 p2
February 2, 2020
combinatoricslattice pointssquare latticelattice
Problem Statement
We call a set of squares with sides parallel to the coordinate axes and vertices with integer coordinates friendly if any two of them have exactly two points in common. We consider friendly sets in which each of the squares has sides of length . Determine the largest possible number of squares in such a friendly set.