special nine-digit number consists of each digit from 1 to 9. The nine-digit number is divisible by 9. If?

Question

you remove the next rightmost digit, the remaining seven-digit number will be divisible by 7. If you remove the next rightmost digit, the remaining six-digit number will be divisible by 6. This process continues to one. What is the original nine-digit number?

Answer 1

Any 9-digit number meeting the other requirements will be divisible by 9, so you can ignore that requirement.

The first number can be anything, since any number is divisible by 1.

The second, fourth, sixth and eighth numbers must be even.

The fifth number must be 5. Which means the first, third, seventh and ninth numbers will be 1, 3, 7, and 9 in some order.

The hardest part will be finding a 7-digit number divisible by 7 that meets all the previous requirements.

By use of an Excel spreadsheet and some brute force, I figured it out!!

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