Question 9
Let $n\gt 2$ be even and let real numbers $x_1,\ldots,x_n$ satisfy
$$\sum_{1\le i\lt j\le n}(x_i-x_j)^2=1.$$
Find the maximum of $\sum_{i=1}^n(x_i-x_{i+1})^2$, where $x_{n+1}=x_1$.
$$\sum_{1\le i\lt j\le n}(x_i-x_j)^2=1.$$
Find the maximum of $\sum_{i=1}^n(x_i-x_{i+1})^2$, where $x_{n+1}=x_1$.