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ASU 083 All Russian MO 1966 game strategy, sings between 1,2,...,20

Source:

June 19, 2019
minimummaximumgame strategycombinatorics

Problem Statement

2020 numbers are written on the board 1,2,...,201, 2, ... ,20. Two players are putting signs before the numbers in turn (++ or āˆ’-). The first wants to obtain the minimal possible absolute value of the sum. What is the maximal value of the absolute value of the sum that can be achieved by the second player?
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