Question 190
We fix an integer $n \geq 3$. For each nonempty subset of the $\{1,2, \ldots, n\}$ set, we consider the arithmetic mean of its elements. Let $S$ be the set of distinct values of these arithmetic media. Determine the lowest absolute value $|a-b|$, when $a$ and $b$ travel through the set $S$ and $a \neq b$.