Slbert and Beatrice play a game with 2021 on a table
Source: 2021 Francophone MO Seniors p2
April 3, 2021
gamecombinatoricsgame strategywinning strategyFrancophone
Problem Statement
Albert and Beatrice play a game. stones lie on a table. Starting with Albert, they alternatively remove stones from the table, while obeying the following rule. At the -th turn, the active player (Albert if is odd, Beatrice if is even) can remove from to stones. Thus, Albert first removes stone; then, Beatrice can remove or stones, as she wishes; then, Albert can remove from to stones, and so on.
The player who removes the last stone on the table loses, and the other one wins. Which player has a strategy to win regardless of the other player's moves?