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Numerical puzzle

  1. Jul 8, 2008 #1
    1. The problem statement, all variables and given/known data
    Im having problem of even starting this question:

    "Determine the positive integer N = abcdef such that 6N = defabc"

    any ideas?

    2. Relevant equations

    3. The attempt at a solution
  2. jcsd
  3. Jul 8, 2008 #2
    [tex]6N = defabc = abcdef = N[/tex]

    6N doesn't equal N unless it's 0. The only solution is 0 which is not a positive integer.

    Or am I missing something really stupid?
  4. Jul 8, 2008 #3
    actually i ended up solving it
    abc = 142 and def = 857

    ....abc and def are just the digits in the question. but thanks!
  5. Jul 8, 2008 #4


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    Homework Helper

    Actually, anyone who recognizes the decimal expansions of 1/7 and 6/7 might suspect immediately that this is an answer... (Ah, but is it unique?)

    Feldoh, this type of puzzle is what is referred to as a cryptarithm. Letters stand in for digits and the prospective solver is supposed to "decode" the arithmetic problem. In classical form, this problem would be posed as

    x 6

    The question does not say that 6N = N , but that 6N is a digital rearrangment of N.
  6. Jul 8, 2008 #5
    Regardless I think the question could be worded better...
  7. Jul 8, 2008 #6


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    Homework Helper

    It did strike me that the intent of the problem might be obscure to anyone not familiar with this kind of puzzle.
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