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Math Help - Finding how many 8 digit numbers, with a twist

  1. #1
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    Question Finding how many 8 digit numbers, with a twist

    I need to find how many 8 digit numbers exists that have no zeros in them and each of the other digits (1-9) may only occur once. (no repeats)

    Also the numbers must be devisable with three.

    Please help, i have been trying to figur this one out for a while but i am really stuck.

    Regards Monika
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    Quote Originally Posted by Monika1987 View Post
    I need to find how many 8 digit numbers exists that have no zeros in them and each of the other digits (1-9) may only occur once. (no repeats) Also the numbers must be divisible with three.
    Any number divisible three must have the sum of its digits divisible by three.
    Note that 1+2+4+5+7+8=27 thus if we add any two of \{3,6,9\} we have an eight-digit number divisible by three.
    Note also that those are the only eight-digit numbers divisible by three.
    Rearrange each set. What is the total?
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