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Just a simple arithmetic problem

  1. Dec 30, 2012 #1

    BobG

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    Easy arithmetic problem:

    [tex]x=222,222,222,222,222,222,222^2-222,222,222,222,222,222,221^2[/tex]

    Find x.
     
  2. jcsd
  3. Dec 30, 2012 #2
    [tex]
    x=(n+1)^2-n^2=2n+1
    [/tex]
    where [itex]n=222,222,222,222,222,222,221[/itex].
    Therefore
    [tex]
    x=444,444,444,444,444,444,443
    [/tex]
     
  4. Jan 2, 2013 #3
    I set N = 222,222,222,222,222,222 so that question becomes

    (n+222)^2 - (n+221)^2

    after which solving for n is straightforward

    Not as nice as the first response, however
     
  5. Mar 11, 2013 #4
    mmm...

    [tex] x=a^2-b^2=(a+b)(a-b) [/tex]
    but [tex] a-b = 1 [/tex] so
    [tex] x = a+b = 444,444,444,444,444,444,443 [/tex]
     
    Last edited: Mar 11, 2013
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