1.1. Masha thought of a 10-digit number and told Vasya that the remainder of dividing this number by 9 is 3. Then Masha crossed out one digit and told Vasya that the remainder of dividing the resulting 9-digit number by 9 is 7. Help Vasya guess the digit that Masha crossed out. Write this digit in the answer.
Answer: 5. Solution. According to the divisibility rule for 9, the remainder of the division of the sum of the digits of the number by 9 is 3 (so the sum of the digits of this number is $9n+3$), and the remainder of the division of the sum of the digits of the resulting number by 9 is 7 (so the sum of the digits of the resulting number is $9k+7$). If the digit that was crossed out is $x$, then $9n+3-x=9k+7$, from which $x=9(n-k)+3-7$, meaning the crossed-out digit is $9+3-7=5$.