Question 18
The odd number of the asterisks are written on the blackboard: $\underbrace{**\dots*}_{2n+1}$.
Ann and Bob play the following game. They, in turn (Ann starts), replace one of the asterisks in the expression $\underbrace{**\dots*}_{2n+1}$ by any of the digits from $0$ to $9$ (the first left asterisk cannot be replaced by $0$). Ann wins if the obtained number is divisible by $11$, otherwise Bob wins.
Who of the players wins if both of them play to win?
Ann and Bob play the following game. They, in turn (Ann starts), replace one of the asterisks in the expression $\underbrace{**\dots*}_{2n+1}$ by any of the digits from $0$ to $9$ (the first left asterisk cannot be replaced by $0$). Ann wins if the obtained number is divisible by $11$, otherwise Bob wins.
Who of the players wins if both of them play to win?