Question 162
Each integer from $1$ to $n$ was colored either red, or blue, and each color was used at least once. It turned out that
* Every red number is a sum of some two distinct blue numbers;
* Every blue number is a difference of some two red numbers.
Find the smallest number $n$ for which such coloring is possible.
* Every red number is a sum of some two distinct blue numbers;
* Every blue number is a difference of some two red numbers.
Find the smallest number $n$ for which such coloring is possible.