# 2023 Australian Mathematics Olympiad — Problem 1

## A nice counting puzzle that anyone can try

# The Problem

Mia is playing the following game. She writes the numbers 1,2,3,…, *n* in some order on the sides of a regular *n*-sided polygon. Then, on each vertex of the polygon, she writes the sum of the numbers on the two sides that meet at that vertex. Mia wins if the *n* numbers…