, 2020

A polyomino is a figure which consists of unit squares joined together by their sides. (A polyomino may contain holes.) Let $n \ge 3$ be a positive integer. Consider a grid of unit square cells which extends to infinity in all directions. Find, in terms of $n$, the greatest positive integer $C$ which satisfies the following condition: For every colouring of the cells of the grid in $n$ colours, there is some polyomino within the grid which contains at most $n - 1$ colours and whose area is at least $C$.