Question 187
Aerith and Bob take turns picking a nonnegative integer, each time subtracting a (positive) divisor from the other's last number. The first person to pick $0$ loses. For example, if Aerith reached $2020$ on some turn, Bob could pick $2020-20=2000$, as $20$ is a divisor of $2020$.
Continuing this example (with Aerith now picking a divisor of $2000$), if both of them play optimally, who wins?
Continuing this example (with Aerith now picking a divisor of $2000$), if both of them play optimally, who wins?