9.1. In a five-digit number, one of the digits was crossed out, and this four-digit number was subtracted from the original number. As a result, the number 54321 was obtained. Find the original number.
Answer: 60356. Solution. Let $x$ be the four-digit number obtained after crossing out a digit. Note that the crossed-out digit was the last digit of the five-digit number, because otherwise the last digit after subtraction would be zero. Let this digit be $y$. We have the equation $10 x+y-x=54321 \Leftrightarrow 9 x+y=54321=9 \cdot 6035+6$. Therefore, $x=6035$ and $y=6$ (the quotient and remainder when 54321 is divided by 9).