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Math Help - parts problem

  1. #1
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    parts problem

    six straight lines are drawn in the plane such that no two lines are parallel and no three lines are concurrent. then the no of parts in which these lines divide are
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  2. #2
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    If you have no intuition for the formula, setup a recurrence and solve.
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  3. #3
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    how to do that
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  4. #4
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    Hint:
    # parts with n+1 lines = # parts with n lines + ???

    Please show some effort in solving the problem in your future posts.
    Also, there are many ways to solve this problem. It would be good if you provide context as to what you have been learning to solve this type of problem.
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  5. #5
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    Quote Originally Posted by snowtea View Post
    Hint:
    # parts with n+1 lines = # parts with n lines + ???

    Please show some effort in solving the problem in your future posts.
    Also, there are many ways to solve this problem. It would be good if you provide context as to what you have been learning to solve this type of problem.
    i got a triangle while drawing three lines
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  6. #6
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    Quote Originally Posted by prasum View Post
    i got a triangle while drawing three lines
    This does not help with the problem. Since it asks nothing about triangles.

    # parts with n+1 lines = # parts with n lines + ???

    How many additional parts are added with each line?
    It is a really simple question. Draw it on a piece of paper, and try to make a good guess.
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  7. #7
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    Also, please tell us the context for your question. So we can better help you solve the problem in the way you understand best.
    Is it for a specific class? Is it for your own curiosity and mathematical enjoyment?
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  8. #8
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    There is a complete detailed discussion of this problem in MATHEMATICS OF CHOICE by Ivan Niven, page 124.
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  9. #9
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    Quote Originally Posted by prasum View Post
    six straight lines are drawn in the plane such that no two lines are parallel and no three lines are concurrent. then the no of parts in which these lines divide are
    The lines are non-parallel, non-concurrent.

    If you have a single line, the line is undivided.
    Total parts is 1.

    A new line crosses the original line and is itself cut in 2 parts.
    Total number of new parts is 3.

    A new line crosses the previous two lines, creating 2 new parts on them,
    while itself is crossed by both of those lines, so it has 3 parts.
    Total number of new parts is 5.

    A new line crosses all of the previous three lines, creating 3 new parts.
    It is itself crossed by all three, so it has 4 parts.
    Total number of new parts is 7.

    There is a pattern to this.
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  10. #10
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    i am sorry the question says in how many parts the lines divide the plane
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  11. #11
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    Beginning with an original plane...

    A new line divides the original plane. Add 1 to number of parts.
    1 new line, 1 new part.

    A new line cuts the previous line, adding 2 new parts.
    2 lines, 2 new parts.

    A new line cuts the 2 previous lines, adding 3 new parts.
    3 lines, 3 new parts.

    A new line cuts the 3 previous lines adding 4 new parts.
    4 lines, 4 new parts.

    etc.
    Last edited by Archie Meade; January 13th 2011 at 10:39 AM. Reason: omitted a piece
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  12. #12
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    Quote Originally Posted by Archie Meade View Post
    Beginning with an original plane...

    A new line divides the original plane. Add 1 to number of parts.
    1 new line, 1 new part.

    A new line cuts the 2 previous lines, adding 3 new parts.
    3 lines, 3 new parts.

    A new line cuts the 3 previous lines adding 4 new parts.
    4 lines, 4 new parts.

    etc.
    thanks
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