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Numbers in the set {-1,1} such that sum of pairs is 999

Source: Pan African Olympiad 2009

October 1, 2011
number theory proposednumber theory

Problem Statement

Determine whether or not there exist numbers x1,x2,…,x2009x_1,x_2,\ldots ,x_{2009} from the set {−1,1}\{-1,1\}, such that: x1x2+x2x3+x3x4+…+x2008x2009+x2009x1=999x_1x_2+x_2x_3+x_3x_4+\ldots+x_{2008}x_{2009}+x_{2009}x_1=999
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