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ASU 056 All Russian MO 1965 min sum of products of x_1,x_2,...,x_n

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June 19, 2019
algebraminimuminequalities

Problem Statement

a) Each of the numbers x1,x2,...,xnx_1,x_2,...,x_n can be 1,01, 0, or −1-1. What is the minimal possible value of the sum of all products of couples of those numbers.
b) Each absolute value of the numbers x1,x2,...,xnx_1,x_2,...,x_n doesn't exceed 11. What is the minimal possible value of the sum of all products of couples of those numbers.
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