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Find the rearrangement

Source: IMO LongList 1982 - P17

September 10, 2010
algebraSequencemaximizationminimizationRearrangementIMO ShortlistIMO Longlist

Problem Statement

(a) Find the rearrangement {a1,…,an}\{a_1, \dots , a_n\} of {1,2,…,n}\{1, 2, \dots, n\} that maximizes a1a2+a2a3+⋯+ana1=Q.a_1a_2 + a_2a_3 + \cdots + a_na_1 = Q.
(b) Find the rearrangement that minimizes Q.Q.
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