9.1. In a three-digit number, the first digit was crossed out, resulting in a two-digit number. If the original number is divided by this two-digit number, the quotient is 9 and the remainder is 8. Find the original number. (Provide all possible solutions.)
Answer: 4 possible numbers: $224 ; 449 ; 674 ; 899$. Solution. Let $x$ be the first digit of the original number, $y$ be the two-digit number after erasing $x$. Then we have the equation $100 x+y=9 y+8 \Leftrightarrow 2 y+2=25 x$. Therefore, $x$ is an even number: $x=2 z$ for some $z(z \leq 4)$. Hence, $y+1=25 z$, and the possible values for the number $y+1$ are: $25 ; 50 ; 75 ; 100$, and the corresponding numbers $x$ are $2 ; 4 ; 6 ; 8$.