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Finding maximum sum of consecutive ten numbers in circle.

Source:

February 8, 2011
invariantinequalities unsolvedinequalities

Problem Statement

Each of 999999 numbers placed in a circular way is either 11 or āˆ’1-1. (Both values appear). Consider the total sum of the products of every 1010 consecutive numbers. (a)(a) Find the minimal possible value of this sum. (b)(b) Find the maximal possible value of this sum.
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