Question 99
Given a positive integer $n$ and an increasing real-valued function $f$ on the closed unit interval $[0, 1]$, determine the maximum value the sum
$$
\sum_{k=1}^{n} f\left(\left|x_k - \frac{2k-1}{2n}\right|\right)
$$
may achieve subject to $0 \le x_1 \le \dots \le x_n \le 1$.
$$
\sum_{k=1}^{n} f\left(\left|x_k - \frac{2k-1}{2n}\right|\right)
$$
may achieve subject to $0 \le x_1 \le \dots \le x_n \le 1$.