1. Find all five-digit numbers where the second digit is five times the first, and the product of all five digits is 1000.
Answer: 15855, 15585, 15558. Solution: The first digit can only be 1, otherwise the second digit will be greater than 9. Then the second digit is 5, and it follows that the product of the last three digits must equal 200. Since $200=5 \times 5 \times 8$, two of these three digits must be 5. But then the third digit must be 8, which gives us the answer.