SE-SKOLORNAS 2000 Problem 1

Each of the numbers $1, 2, ... , 10$ is colored red or blue. $5$ is red and at least one number is blue. If $m, n$ are different colors and $m+n \le 10$ , then $m+n$ is blue. If $m, n$ are different colors and $mn \le 10$ , then $mn$ is red. Find all the colors.