Question 162
Aerith and Bob take turns picking a nonnegative integer, each time changing exactly one digit from the other's last number. The first person to pick a number that (s)he picked before loses. If Aerith goes first, and both play optimally, who wins?
(Note: There are no leading zeroes, except in the number $0$ itself. For instance, if one person picks $2020$, the other could respond by picking $0020=20$, however the reverse does not hold.)
(Note: There are no leading zeroes, except in the number $0$ itself. For instance, if one person picks $2020$, the other could respond by picking $0020=20$, however the reverse does not hold.)