Question 2
Let $x_1 \le x_2 \le \dots \le x_{100}$ be real numbers such that $|x_1| + |x_2| + \dots + |x_{100}| = 1$ and $x_1 + x_2 + \dots + x_{100} = 0$. Among all such 100-tuples of numbers, the greatest value that $x_{76} - x_{16}$ can achieve is $\frac{m}{n}$, where $m$ and $n$ are relatively prime positive integers. Find $m+n$.