MathDB

3

Part of 2018 APMO

Problems(1)

Tri-connected squares

Source: APMO 2018 P3

6/24/2018
A collection of nn 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 PP in common, then PP is a vertex of each of the squares. (iii) Each square touches exactly three other squares.
How many positive integers nn are there with 2018≤n≤30182018\leq n \leq 3018, such that there exists a collection of nn squares that is tri-connected?
combinatoricsAPMO