# Number Digits Problem #2

Form a number from the digits 0 to 9 such that the first digit is divisible by one, the first two digits form a number that is divisible by two, the first three digits form a number that is divisible by three, and so forth.

I’ll post my solution in a day or two.

HT: QYV

## 3 thoughts on “Number Digits Problem #2”

1. I brute forced my way to an 12-digit number then had to stop. But I’m sure if I looked at it more I could find a longer one.

204000327084
also tried
804000402048

It would be nice to see your method.

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2. mathercize says:

Did we need to use the numerals once each? And, by ‘first digit’ do you mean ‘reading it from left to right’, or do you mean ‘in the ones place’? I assumed the former.

If I understood correctly, I came up with 720054324, but I don’t think its unique. I really just started with 7 and went down the list of choosing numbers that worked.

The method directly above was only done after I created a list of equations, domain restrictions, and conclusions based on them (including that if the number were abcdefghi, then e must be 0 or 5, while (a+b+c) must be divisible by 3, etc). This seemed to open-ended, so I decided to just guess some numbers.

Like I said, I don’t think my solution is unique. I didn’t double-check it, but I think 321204168 works as well.

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