MathDB

3

Part of 2023 Iberoamerican

Problems(1)

Weighting options in Brazil

Source: IberoAmerican 2023, Day 1, P3

9/8/2023
Ann and Beto play with a two pan balance scale. They have 20232023 dumbbells labeled with their weights, which are the numbers 1,2,…,20231, 2, \dots, 2023, with none of them repeating themselves. Each player, in turn, chooses a dumbbell that was not yet placed on the balance scale and places it on the pan with the least weight at the 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 win. Determine which of the players has a winning strategy and describe the strategy.
combinatorics