1997 PMWC Problems/Problem T9

Problem

Find the two $10$ -digit numbers which become nine times as large if the order of the digits is reversed.

This problem needs a solution. If you have a solution for it, please help us out by adding it. Let's call any number that satisfies $x$ .

1. $1000000000\le x\le1111111111$ . It must be $10$ -digit, and it multiplied by nine must be $10$ -digit.

2. $x$ divides by $9$ . If you recall the divisibility rule of 9, the sum of digits must be divisible by 9.

3. $x$ ends in $9$ . $9x$ must start with $9$ .

4. So $1000000089\le x\le 1111111119$

5. $12345670$ numbers to go.