Minimum sum of the squares Find the smallest value of the expression
$$(x_1-x_2)^2+(x_2-x_3)^2+...+(x_{n-1}-x_n)^2+(x_n-x_1)^2,$$
if $x_1,x_2,...,x_n -$ pairwise different integers
My work so far:
I have a hypothesis, that the answer is: $1+1+..+1+(n-1)^2=(n-1)+(n-1)^2=(n-1)n$, 
but I do not know how to prove it

Building off of gammatester's counterexample, it looks like a correct conjecture might be to run up the odds and down the evens, e.g.,
$$1,3,5,7,9,10,8,6,4,2$$
Note that no matter how you arrange the numbers, the average difference between (circularly) consecutive numbers is always $0$, so in a sense what you're trying to do is find an arrangement that minimizes the variance. I.e., if you fix a circular arrangement and let $X$ be the random variable for the difference between a randomly chosen pair of consecutive numbers, then $V(X)=E(X^2)-E(X)^2=E(X^2)-0$.
