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2player game, n-> n+1 or n-> n/2

Source: Chile Finals 2007 L2 p3

October 3, 2022
number theorycombinatoricsgamegame strategy

Problem Statement

Two players, Aurelio and Bernardo, play the following game. Aurelio begins by writing the number 11. Next it is Bernardo's turn, who writes number 22. From then on, each player chooses whether to add 11 to the number just written by the previous player, or whether multiply that number by 22. Then write the result and it's the other player's turn. The first player to write a number greater than 2007 2007 loses the game. Determine if one of the players can ensure victory no matter what the other does.