MathDB

Let

n\ge 3

be an integer. Annalena has infinitely many cowbells in each of

n

different colours. Given an integer

m \ge 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

Problem Statement