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 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 . Then the sum written on the board is calculated. If the result is a multiple of , Jose wins the game, if not, Maria wins. Determine which of the two has a winning strategy.