Question 39
On the occasion of the 47th Mathematical Olympiad 2016 the numbers $47$ and $2016$ are written on the blackboard. Alice and Bob play the following game. Alice begins and in turns they choose two numbers $a$ and $b$ with $a \gt b$ written on the blackboard, whose difference $a - b$ is not yet written on the blackboard and write this difference additionally on the board. The game ends when no further move is possible. The winner is the player who made the last move.
Prove that Bob wins, no matter how they play.
Prove that Bob wins, no matter how they play.