Question 176
Determine all ways to color in green and red the numbers $1, 2, \ldots, 10$ such that the following conditions are fulfilled:
a) the number $5$ is colored red;
b) if the numbers $x$ and $y$ have different colors and $x + y \le 10$, then the number $x + y$ must be colored green;
c) if the numbers $x$ and $y$ have different colors and $xy \le 10$, then the number $xy$ must be colored red.
a) the number $5$ is colored red;
b) if the numbers $x$ and $y$ have different colors and $x + y \le 10$, then the number $x + y$ must be colored green;
c) if the numbers $x$ and $y$ have different colors and $xy \le 10$, then the number $xy$ must be colored red.