IMO 1982 — Shortlisted Problems Question 11

B5 (CAN 3). (a) Find the rearrangement $\{a_1,\ldots,a_n\}$ of $\{1,2,\ldots,n\}$ that maximizes
$$a_1a_2+a_2a_3+\cdots+a_na_1=Q.$$
(b) Find the rearrangement that minimizes $Q$.