Number Digits Problem #2

image 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.


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.

    also tried

    It would be nice to see your method.


  2. 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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