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Discret mathematics problem

  1. Apr 17, 2007 #1
    Given n marbles arrayed in a square with n+1 slots(slot n+1 being empty(labelled with numbers from 1 to n+1) you have to bring them all from their orginal positions to a position in whcih bringing them back woudl take the most moves. The rule is to move each marble to the adjacent square.


    I'm really not sure as to how to solve it. I'm really just doing this because I saw it and the fact that i don't know the solution is killing me.


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  2. jcsd
  3. Apr 17, 2007 #2

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    It's kind of hard to understand what you're saying, but it seems like what you're describing is essentially the fifteen puzzle.
     
    Last edited: Apr 17, 2007
  4. Apr 17, 2007 #3
    Yes its just that and I'd like to know how to prove what combination requires the greatest number of moves.
     
  5. Apr 18, 2007 #4

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    According to that page:

    So I'm guessing there's no easy answer to your question.
     
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