Question 89
Let $n \ge 2$ be an integer. Suppose that real numbers $a_1, a_2, \dots, a_{2n}$ satisfy $|a_k - a_{n+k}| \ge 1$ for every integer $k$ such that $1 \le k \le n$. Find the minimum possible value of
$$
(a_1 - a_2)^2 + (a_2 - a_3)^2 + \dots + (a_{2n-1} - a_{2n})^2 + (a_{2n} - a_1)^2.
$$
$$
(a_1 - a_2)^2 + (a_2 - a_3)^2 + \dots + (a_{2n-1} - a_{2n})^2 + (a_{2n} - a_1)^2.
$$