Question 156
Let $n \gt 3$ be a positive integer and let $T$ denote the set of the first $n$ positive integers. A subset $S$ of $T$ is called a *scattered set* if $S$ has the following property: There exists a positive integer $c$, not exceeding $\frac{n}{2}$ such that $|s_1 - s_2| \neq c$ for any two numbers $s_1, s_2$ in $S$. What is the maximum number of elements of a scattered set?