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Math Help - stuck at this problem for more than two hours...

  1. #1
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    stuck at this problem for more than two hours...

    It is given that there are at least 1680 ways of painting m different colours into 4 different regions.

    Show that m^2 - 3m - 40 >= 0 (Hint: x^2 - 3x + 42 > 0 for all real values of x)

    How to show....

    have been stuck by this problem for two hours... big headache
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  2. #2
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    Re: stuck at this problem for more than two hours...

    Quote Originally Posted by kennysiu View Post
    It is given that there are at least 1680 ways of painting m different colours into 4 different regions.

    Show that m^2 - 3m - 40 >= 0 (Hint: x^2 - 3x + 42 > 0 for all real values of x)
    What does "at least 1680 ways of painting m different colours into 4 different regions" mean?
    Does order matter? Can a colour be repeated? What about rotations.
    You have not fully described the question.
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  3. #3
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    Re: stuck at this problem for more than two hours...

    Quote Originally Posted by Plato View Post
    What does "at least 1680 ways of painting m different colours into 4 different regions" mean?
    Does order matter? Can a colour be repeated? What about rotations.
    You have not fully described the question.
    order does matter so it is permutation. Colour cannot be repeated. I don't understand what you mean by rotation. Never encounter such a term.
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  4. #4
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    Re: stuck at this problem for more than two hours...

    Quote Originally Posted by kennysiu View Post
    order does matter so it is permutation. Colour cannot be repeated. I don't understand what you mean by rotation. Never encounter such a term.
    m(m-1)(m-2)(m-3)\ge 1680 has m\ge 8 as a solution.

    Note m^2-3m-40=(m-8)(m+5).
    Attached Thumbnails Attached Thumbnails stuck at this problem for more than two hours...-untitled.gif  
    Last edited by Plato; April 13th 2012 at 01:54 PM.
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