Task 1. Gjorgja's phone number consists of two three-digit numbers written side by side. Each of them is divisible by 45, and the middle digit is 8. Determine the phone number, if the three-digit number written from left in the phone number is smaller than the three-digit number from the right.
Solution. Let the phone number be $\overline{a 8 b c 8 d}$. If each number $\overline{a 8 b}$ and $\overline{c 8 d}$ is divisible by 45, then they must be divisible by 5 and by 9. It follows that the last digit is 5 or 0. If the last digit is 5, then the first digit must also be 5, since only 585 is divisible by 9. If the last digit is 0, then the first digit is 1. Since the first number (written from left) is smaller, the desired number is 180585.