Question 171
Aoife and Zoe play a game. On each of Aoife's three turns, Aoife replaces one of the asterisks in the expression $**********$ with one of the digits $1$, $2$, $3$, $4$, $5$, $6$, $7$, $8$, $9$ that has not yet been used. At Zoe's turn she can replace two of the asterisks with two different digits not yet selected. Aoife starts and the players take alternate turns. Zoe wins if the final number is a multiple of $27$. Does Zoe have a winning strategy?