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Math Help - prove that ...

  1. #1
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    prove that ...

    take any 3-digit integer, reverse its digits, and subtract.
    For example 742-247 = 495

    This difference is divisible by 9.

    Prove that, this must happen for all 3-digit numbers

    Thank you in advance
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  2. #2
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    Joined
    Oct 2008
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    SOLUTION

    Any 3 digit number can be represented as
    100x + 10y + z and its reverse would be
    100z + 10y - x

    Their difference would be
    100(x-z) + (z-x) which can be written as 99(x-z).


    99(x-z) is always divisable by 9

    TRUE?
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