Question 4
Select as many integers as possible from $1$ to $21$ so that no two disjoint pairs have the same difference. For example $\{1,3,5,13\}$ is such a collection; since the two pairs $3-1=5-3$ are not disjoint. On the other hand, $\{1,2,4,7,10\}$ is not since $4-1=10-7$. What is the maximum number of integers that can be selected?