2023 OIM Problems/Problem 3

Problem

Ana and Beto play with a two pan balance scale. They have 2023 dumbbells labeled with their weights, which are the numbers 1, 2, . . . , 2023, with none of them repeating themselves. Each player, in turn, chooses a dumbbell that was not yet placed on the balance and places it on the pan with the least weight at that moment. If the scale is balanced, the player places it on any pan. Ana starts the game, and they continue in this way alternately until all the dumbbells are placed. Ana wins if at the end the scale is balanced, otherwise Beto wins. Determine which of the players has a winning strategy and describe the strategy.

Solution

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See also

https://sites.google.com/associacaodaobm.org/oim-brasil-2023/pruebas