Question 78
Let $M(n)$ be the minimum number of cells that must be coloured in the $6 \times n$ square grid to ensure that every $2 \times 3$ rectangle (in any orientation) contains a coloured cell. Is it true that $M(n) = p_n + k_n^3$ for all $n \ge 2$ where $p_n$ is a prime and $k_n$ is a nonnegative integer?