Question 53
Alice and Bob play a game. Starting from Alice, two guys take turns to choose a digit from $1$ to $9$ without repetition, and put them from the leftmost to the rightmost to form a $7$-digit integer (i.e., $\overline{A_1B_2A_3B_4A_5B_6A_7}$). If there exists a perfect $7$th-power that ends in these $7$ digits, then Alice wins; otherwise, Bob wins. Who has the winning strategy?