NL-NWO 2018 Problem 2

The numbers $1$ to $15$ are each coloured blue or red. Determine all possible colourings that satisfy the following rules: • The number $15$ is red. • If numbers $x$ and $y$ have different colours and $x + y \le 15$ , then $x + y$ is blue. • If numbers $x$ and $y$ have different colours and $x \cdot y \le 15$ , then $x \cdot y$ is red.