PAMO 2009 Problem 1

Day 1

Determine whether or not there exist numbers $x_1,x_2,\ldots ,x_{2009}$ from the set $\{-1,1\}$ , such that: $x_1x_2+x_2x_3+x_3x_4+\ldots+x_{2008}x_{2009}+x_{2009}x_1=999$

Dataset text AI-MO AoPS. Quoted with source.

Official text: Pan-African Mathematics Olympiad 2009 official paper, page 1.

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