7.3. Masha and Sasha take turns (starting with Masha) writing 10 digits on the board from left to right to form a ten-digit number. Moreover, it is not allowed to write two consecutive identical digits. If the resulting number is divisible by 9, then Sasha wins; otherwise, Masha wins. Who will win with correct play from both sides?
Answer: Sasha.

Solution. A number is divisible by 9 if the sum of its digits is divisible by 9. Therefore, one of Sasha's possible strategies is to complement each of Masha's digits to 9. That is, if Masha writes 0, then Sasha writes 9; if Masha writes 1, then Sasha writes 8, and so on. Thus, after each pair of moves, the sum of the digits will increase by 9. By the time the entire number is written, it will be equal to $9 \cdot 5=45$.