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ASU 077 All Russian MO 1966 s=\pm a1\pm a2\pm ...\pm a_n

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June 19, 2019
algebra

Problem Statement

Given the numbers a1,a2,...,ana_1, a_2, ... , a_n such that 0≤a1≤a2≤2a1,a2≤a3≤2a2,...,an−1≤an≤2an−10\le a_1\le a_2\le 2a_1 , a_2\le a_3\le 2a_2 , ... , a_{n-1}\le a_n\le 2a_{n-1} Prove that in the sum s=±a1±a2±...±ans=\pm a1\pm a2\pm ...\pm a_n You can choose appropriate signs to make 0≤s≤a10\le s\le a_1.
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