Question 22
Two players, Abigail and Zoe, play a game. Abigail chooses an odd number less than $800$ and writes it on the blackboard. Zoe now chooses a different odd number less than $1200$ and writes it on the blackboard. Each in turn replaces their number by the difference between their number and the smallest power of $2$ bigger than their number. If both players reach $1$ on the same move the game is drawn. If not, the player who first reaches $1$ loses.
Who has the winning strategy?
Who has the winning strategy?