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2019 different positive integers on the blackboard, winning strategy

Source: 2nd Mathematics Regional Olympiad of Mexico Northwest 2019 P1

September 6, 2022
combinatoricswinning strategy

Problem Statement

Jose and Maria play the following game: Maria writes 20192019 positive integers different on the blackboard. Jose deletes some of them (possibly none, but not all) and write to the left of each of the remaining numbers a sign ++or a sign āˆ’-. Then the sum written on the board is calculated. If the result is a multiple of 20192019, Jose wins the game, if not, Maria wins. Determine which of the two has a winning strategy.