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Regional Olympiad - FBH 2018 Grade 11 Problem 2

Source: Regional Olympiad - Federation of Bosnia and Herzegovina 2018

September 18, 2018
SumSequencealgebra

Problem Statement

Let a1,a2,...,a2018a_1, a_2,...,a_{2018} be a sequence of numbers such that all its elements are elements of a set {−1,1}\{-1,1\}. Sum S=∑1≤i<j≤2018aiajS=\sum \limits_{1 \leq i < j \leq 2018} a_i a_j can be negative and can also be positive. Find the minimal value of this sum
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