2021 IMO Shortlist Problems/C2
Problem
Let 
be an integer. An integer 
is called 
-colourful if, given infinitely
many marbles in each of colours 
, it is possible to place 
of them around a circle so that in any group of 
consecutive marbles there is at least one marble of colour 
for each 
. Prove that there are only finitely many positive integers which are not -colourful. Find the largest among them.
