Question 146
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 $2018 \le n \le 3018$ such that there exists a collection of $n$ squares that is tri-connected?
(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 $2018 \le n \le 3018$ such that there exists a collection of $n$ squares that is tri-connected?