(a) Find the rearrangement $\{a_1, \dots , a_n\}$ of $\{1, 2, \dots, n\}$ that maximizes \[a_1a_2 + a_2a_3 + \cdots + a_na_1 = Q.\] (b) Find the rearrangement that minimizes $Q.$
Problem
Source: IMO LongList 1982 - P17
Tags: algebra, Sequence, maximization, minimization, Rearrangement, IMO Shortlist, IMO Longlist