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Missing digit

  1. Dec 3, 2004 #1

    BobG

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    I have a five digit number - no, it's not that easy
    I rearrange the digits and subtract the smaller number from the larger.

    The difference is also a five digit number. I jumble up the digits of the difference. Four of the digits of the difference are 2172.

    What's the missing digit of the difference?
     
    Last edited: Dec 3, 2004
  2. jcsd
  3. Dec 4, 2004 #2
    brute force , hapahazard hand waving and abra cadabras are giving me the missing digit as ::6::

    Let me see if i can see through some technique here ....
    interesting problem btw.

    -- AI
     
  4. Dec 4, 2004 #3

    Tide

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    The missing digit would have to be 6 since the difference must be a multiple of 9.
     
  5. Dec 4, 2004 #4
    duh! ofcourse!

    -- AI
    **i should sincerely stop playing notpron, i am losing sight of the obvious**
     
  6. Dec 5, 2004 #5
    i'm missing something, why does it have to be a multiple of 9?
     
  7. Dec 5, 2004 #6
    Remember (10^k - 1) is always multiple of 9.
    So, for each digit A , you have:
    A*10^n - A*10^m = A*(10^n - 10^m) which is multiple of 9 .
     
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