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Math Help - Combinatorics/Orders Problem? NEED HELP PLEASE PLEASE PLEASE

  1. #1
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    Combinatorics/Orders Problem? NEED HELP PLEASE PLEASE PLEASE

    Several children were playing in the ugly tree when suddenly they all fell.
    Roger hit branches A, B, and C in that order on the way down.
    Sue hit branches D, E, and F in that order on the way down.
    Gillian hit branches G, A, and C in that order on the way down.
    Marcellus hit branches B, D, and H in that order on the way down.
    Juan-Phillipe hit branches I, C, and E in that order on the way down.
    Mikey hit every branch A through I on the way down. Given only this information, in
    how many different orders could he have hit these 9 branches on the way down?
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  2. #2
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    Re: Combinatorics/Orders Problem? NEED HELP PLEASE PLEASE PLEASE

    gabicdefh
    gaibcdefh
    giabcdefh
    igabcdefh
    Last edited by MaxJasper; October 16th 2012 at 08:36 PM.
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  3. #3
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    Re: Combinatorics/Orders Problem? NEED HELP PLEASE PLEASE PLEASE

    Thanks. So those are the only four orders?
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  4. #4
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    Re: Combinatorics/Orders Problem? NEED HELP PLEASE PLEASE PLEASE

    Unless others find more!
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  5. #5
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    Re: Combinatorics/Orders Problem? NEED HELP PLEASE PLEASE PLEASE

    Thanks. Is there a reason that you put all the gs first? I mean why could it not just be abcdefgh? Once again thanks a lot
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    Senior Member MaxJasper's Avatar
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    Re: Combinatorics/Orders Problem? NEED HELP PLEASE PLEASE PLEASE

    G>A>C
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    Re: Combinatorics/Orders Problem? NEED HELP PLEASE PLEASE PLEASE

    This got me curious. Is there a truly mathematical way of developing an answer? Just a curiosity. I was wondering if somehow you could list the branches in order, and resolve an answer without manually counting all of the possibilities.
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    Re: Combinatorics/Orders Problem? NEED HELP PLEASE PLEASE PLEASE

    Yes there is a way to develop the answer mathematically. Word the question like this.

    Mikey has 9 cards in front of him, in how many different ways can he pick up the 9 cards?

    Well....

    1,2,3,4,5,6,7,8,9
    1,2,3,4,5,6,7,9,8
    1,2,3,4,5,6,8,9,7
    ect. You should have been taught about factorials. The factorial of a number is calculated as.

    9! = 1\cdot2\cdot3\cdot4\cdot5\cdot6\cdot7\cdot8\cdot9

    You'll most certainly need a calculator because factorials grow at an insane rate for each digit you add. Go ahead and type that into your calculator.

    P.S The branch example is a terribly worded question because one can assume you can't hit branch I before hitting branch A. So if one falls one can only hit the branches in letter order progressing alphabetically.
    Last edited by uperkurk; October 17th 2012 at 05:13 PM.
    Thanks from xXplosionZz
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    Re: Combinatorics/Orders Problem? NEED HELP PLEASE PLEASE PLEASE

    Quote Originally Posted by MaxJasper View Post
    gabicdefh
    gaibcdefh
    giabcdefh
    igabcdefh
    It seems to me there are some missing possibilities.

    How about

    I G A B D H C E F

    for example?
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  10. #10
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    Reply - part 1

    Hello, Makaveli!

    Several children were playing in the ugly tree when suddenly they all fell.
    Roger hit branches A, B, and C in that order on the way down.
    Sue hit branches D, E, and F in that order on the way down.
    Gillian hit branches G, A, and C in that order on the way down.
    Marcellus hit branches B, D, and H in that order on the way down.
    Juan-Phillipe hit branches I, C, and E in that order on the way down.
    Mikey hit every branch A through I on the way down.
    Given only this information, in how many different orders
    could he have hit these 9 branches on the way down?

    I have this diagram.
    Reading from left to right, we have the branches from the top down.

    \begin{array}{ccccccccccc}&&&& I \\ &&&&& \searrow \\ &&&&&& C \\ &&&&& \nearrow && \searrow \\ G & \to & A & \to & B &&&& E & \to & F \\ &&&&& \searrow && \nearrow \\ &&&&&& D \\ &&&&&&& \searrow \\ &&&&&&&& H \end{array}


    We know that I is somewhere above C.
    I could be above G, between G and A, between A and B, or between B and C.

    We know that D is between B and E.
    D could be between B and C or between C and E.
    . . [To be continued]
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  11. #11
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    Re: Reply - part 2


    We know that H is below D.
    H could be between D and E, between E and F, or below F.

    There are more than 4 possible orders.


    Once again, the program would not let me complete my post.
    I clicked on PREVIEW and got a preview of what I had styped.
    But my work screen was blank and frozen.
    I could not enter anything on it.
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  12. #12
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    Re: Combinatorics/Orders Problem? NEED HELP PLEASE PLEASE PLEASE

    Would a simple nCr function work to some extent, to help to figure out the number of combinations maybe ?
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  13. #13
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    Re: Combinatorics/Orders Problem? NEED HELP PLEASE PLEASE PLEASE

    Could someone please figure this out and show me how they got the answer please? My test is on Sunday, I have to go into school to take it. Thanks so much.
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