Two players, Aurelio and Bernardo, play the following game. Aurelio begins by writing the number 1. Next it is Bernardo's turn, who writes number 2. From then on, each player chooses whether to add 1 to the number just written by the previous player, or whether multiply that number by 2. Then write the result and it's the other player's turn. The first player to write a number greater than 2007 loses the game. Determine if one of the players can ensure victory no matter what the other does. number theorycombinatoricsgamegame strategy