MathNet 2003 — Part 01 Question 133

Let $a_1, a_2, \dots, a_{2n}$ be real numbers with $\sum_{i=1}^{2n-1} (a_{i+1} - a_i)^2 = 1$. Find the maximum value of $(a_{n+1} + a_{n+2} + \dots + a_{2n}) - (a_1 + a_2 + \dots + a_n)$. (posed by Leng Gangsong)