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Math Help - seats

  1. #1
    Member Veronica1999's Avatar
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    seats

    Ten women sit in 10 seats in a line. All of the 10 get up and then reseat
    themselves using all 10 seats, each sitting in the seat she was in before or aseat next to the one she occupied before. In how many ways can the women be reseated?


    seats-seats.jpg

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  2. #2
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    Re: seats

    Quote Originally Posted by Veronica1999 View Post
    Ten women sit in 10 seats in a line. All of the 10 get up and then reseat
    [FONT=CMR10][SIZE=2][FONT=CMR10][SIZE=2][LEFT]themselves using all 10 seats, each sitting in the seat she was in before or aseat next to the one she occupied before. In how many ways can the women be [SIZE=4]reseated?
    Suppose that S_n is the number of ways to seat n women according to the rules.
    Then S_1=1,~S_2=2 and if n\ge 3 then S_n=S_{n-2}+S_{n-1}

    Can you explain why that works?
    Hint: think about using strings already used.
    Last edited by Plato; March 5th 2012 at 01:41 PM.
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  3. #3
    Member Veronica1999's Avatar
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    Re: seats

    seats-seating.jpg
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