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2 player nim game

  1. Dec 26, 2006 #1
    Hi all, ok there are 3 piles containing objects; Pile A, Pile B and Pile C.

    Let the Nim-sum of all 3 piles be denoted as X.

    Let Pile A and Pile B and Pile C contain objects.
    ( In Nim-Sum )

    A + X = D

    B + X = E

    C + X = F

    As we are currently in research of a math project, we are wondering if there is a case whereby D > A, E > B, and F > C. If not, what is the proof?
     
  2. jcsd
  3. Dec 26, 2006 #2

    HallsofIvy

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    Perhaps I am not understanding the question. The number of objects in each pile are A, B, C respectively. What do you mean by "Nim-sum"? Certainly if X> 0 then it must be the case that D> A, E> B, and F> C.
     
  4. Dec 26, 2006 #3

    CRGreathouse

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    I don't know what a Nim-Sum is, but from what you have
    [tex]D>A\Leftrightarrow E>B\Leftrightarrow F>C\Leftrightarrow X>0[/tex]

    so you're just asking if the Nim-Sum is always negative. Well, define it for us and we'll see!
     
    Last edited: Dec 26, 2006
  5. Dec 26, 2006 #4
    According to wikipedia, a nim-sum is an operation used in game theory.
     
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