# Winning strategy

Is there a winning strategy for player one or two in the following scenario: The game begins with the number 2012. In one turn, a player can subtract from the current number any natural number less than or equal to it that is a power of 2. The player who reaches 0 wins.

• so for a slow winning game subtract $1$ or $2$ each time and for a fast winning game subtract $2^{\lfloor \log_2 n \rfloor}$ or $2^{\lfloor \log_2 n \rfloor - 1}$ each time Jun 14, 2012 at 19:45