MathDB

A collection of

n

squares on the plane is called tri-connected if the following criteria are satisfied:
(i) All the squares are congruent. (ii) If two squares have a point

P

in common, then

P

is a vertex of each of the squares. (iii) Each square touches exactly three other squares.
How many positive integers

n

are there with

2018\leq n \leq 3018

, such that there exists a collection of

n

squares that is tri-connected?

Problem Statement