Question 46
Let $n \geq 3$ be an integer. Annalena has infinitely many cowbells in each of $n$ different colours. Given an integer $m \geq n+1$ and a group of $m$ cows standing in a circle, she is tasked with tying one cowbell around the neck of every cow so that every group of $n+1$ consecutive cows have cowbells of all the possible $n$ colours. Prove that there are only finitely many values of $m$ for which this is not possible and determine the largest such $m$ in terms of $n$.