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Math Help - Ascending Numbers Problems

  1. #1
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    Exclamation Ascending Numbers Problems

    We say a number is ascending if it's digits are strictly increasing. For example, 189 and 3468 are ascending while 142 and 466 are not. For which ascending number n is 6n also ascending?

    I have got the answer to this problem after a while with some guess and check, but I would like to know a quicker way to work it out with a proper method. Can you please provide a relatively detailed explanation.

    Thanks in advance
    Atrey
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  2. #2
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    Re: Ascending Numbers Problems

    578 * 6 = 3468 (only tried 3digit numbers; that's the only one)

    Easy enough with a looper program, like:
    loop a from 1 to 7
    loop b from a+1 to 8
    loop c from b+1 to 9
    u = 100a + 10b + c
    v = u*6
    are v's digits in ascending order?

    As far as a "method" goes, you'd need to start by setting up "u" something like (if 3digit number):
    u = 100a + 10(a+w) + a+w+x
    So u = 111a + 11w + x where 8>a>0 and a+w+x<10

    Does 666a + 66w + 6x = an ascending 3digit or 4digit number?

    Perhaps someone here with "number theory expertise" can help you further...I can't
    Thanks from Atrey_G
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  3. #3
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    Re: Ascending Numbers Problems

    Thank you for explaining a logical way to do this problem quicker
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