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Math Help - Mixed-Up Math Puzzle!

  1. #1
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    Mixed-Up Math Puzzle!

    The math department decided they needed new books, and sent in an order. When they got the books back from the printers, however, they discovered that there had been a horrible mistake. Apparently the printer scrambled up all the digits in the printing press, so all the numbers reflected wrong digits. Yet somehow, these mistakes were consistent throughout the book. (For example, all instances of the digit "2" would instead use the digit "7"... but that's just an example! Don't assume that that is a clue for this puzzle!)

    Some examples that were printed in the book were:

    518 x 70 = 6270

    6481 + 3294 = 32847

    7221 x ( 3334 + 3666 ) = ?

    Using this numbering system, what would this book list as the answer to the problem 7221 x ( 3334 + 3666 )?


    I got 0081497 (translated into the mixed-up digits)... from 4467582. Somehow, that seems wrong, though.
    Last edited by blacksuzaku; April 11th 2007 at 10:22 PM.
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  2. #2
    Senior Member ecMathGeek's Avatar
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    Quote Originally Posted by blacksuzaku View Post
    The math department decided they needed new books, and sent in an order. When they got the books back from the printers, however, they discovered that there had been a horrible mistake. Apparently the printer scrambled up all the digits in the printing press, so all the numbers reflected wrong digits. Yet somehow, these mistakes were consistent throughout the book. (For example, all instances of the digit "2" would instead use the digit "7"... but that's just an example! Don't assume that that is a clue for this puzzle!)

    Some examples that were printed in the book were:

    518 x 70 = 6270

    6481 + 3294 = 32847

    7221 x ( 3334 + 3666 ) = ?

    Using this numbering system, what would this book list as the answer to the problem 7221 x ( 3334 + 3666 )?


    I got 0081497 (translated into the mixed-up digits)... from 4467582. Somehow, that seems wrong, though.
    Very fun problem. Not the easiest thing to do.

    The answer is
    8706169 (mixed up digets) = 6249798 (real numbers)
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  3. #3
    Senior Member ecMathGeek's Avatar
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    For the sake of completeness, here are the values of each number:

    (mixed up number) = real number

    (0) = 4
    (1) = 7
    (2) = 0
    (3) = 1
    (4) = 5
    (5) = 3
    (6) = 9
    (7) = 2
    (8) = 6
    (9) = 8
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