## APMO 2018 Problem 3

Discussion on Asian Pacific Mathematical Olympiad (APMO)
samiul_samin
Posts: 999
Joined: Sat Dec 09, 2017 1:32 pm

### APMO 2018 Problem 3

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?