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Maths Quiz!

  1. Sep 3, 2003 #1

    jcsd

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    Okay Maths quiz! normal rules apply (first to answer question correctly gets to ask the next question, etc.):

    1) √(5 + √(24)) = ? in exact surd form
     
    Last edited: Sep 3, 2003
  2. jcsd
  3. Sep 3, 2003 #2

    Hurkyl

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    That font doesn't work for me. :frown:
     
  4. Sep 3, 2003 #3

    jcsd

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    Font corrected :)
     
  5. Sep 3, 2003 #4

    Hurkyl

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    You looking for something like

    √2 + √3

    ?
     
  6. Sep 3, 2003 #5

    jcsd

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    Correct!
     
  7. Sep 3, 2003 #6

    Hurkyl

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    Hrm, my favorite math puzzle is a picture puzzle, but that'd be too hard to describe in words. :frown:


    Ok, here's one:

    A carpeting company has taken an order to carpet an annulus-shaped room (the region between two cocentric circles)... however their drunken surveyor only measured the length of the longest straight line that can be drawn in the room! The manager complained to the resident mathematician about the problem, because this measurement didn't seem to be enough to find the area of the floor, but the mathematician said "But there's a formula for that..." to which the manager responded "Oh, there is? I know what it is then" and walked away.

    What is the formula?
     
  8. Sep 3, 2003 #7

    jcsd

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    πl2/2 ?
     
  9. Sep 3, 2003 #8

    Hurkyl

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    not quite!
     
  10. Sep 3, 2003 #9

    jcsd

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    3πl2/4?
     
  11. Sep 3, 2003 #10

    Hurkyl

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    nope!
     
  12. Sep 3, 2003 #11

    Integral

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    Here is how I see it.
    R= Radius of Large circle
    r= radius of small concentric circle
    D = measurement.

    The measured distance must be tangent to the smaller circle so we have
    ;
    The Radius of the larger circle is the Hypotenuse of a right triangle with sides r and D/2 so

    (D/2)2 = (R2 -r2)= D2/4

    The Area we need is:
    A = [pi] R2-[pi]r2
    A = [pi](R2-r2)
    so
    A = [pi]D2/4
     
  13. Sep 3, 2003 #12

    ahrkron

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    Since (according to the local mathematician) D is enough information to obtain the area, we have to conclude that the result is independent of R and r, which means that we can choose whichever values we like. Using r=0, we have that R = D/2, and the area is [pi]R2, or [pi](D/2)2, and should be the result for all cases.
     
  14. Sep 4, 2003 #13

    marcus

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    If Maths Quiz is played according to similar rules to Astronomy Q/
    A then Hurkyl should speak up and say it is Integral's turn because he was the "first to answer question correctly"

    And if anybody forgets to do what theyre supposed to do, according to the Nicool rules after "2 or 3 days" someone can
    do what's needed to keep the game going. Like, just go ahead and ask another question.

    Because JCSD started the gamethread he can decide on how to adapt Nicool's rules as necessary (which are in Nicool's post at the start of the Astronomy gamethread)

    Those were both neat quiz questions I hope Hurkyl shows up presently, and awards Ahrkron an honor point for elegance
     
  15. Sep 4, 2003 #14

    jcsd

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    It's annoying because I had the right answer but I worked it out using a very roundabout method (using chords and tangents) and I made a mistake :(
     
  16. Sep 4, 2003 #15

    Integral

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    I agree with this. Mine is a brute force solutoion. Hurkyl arrived at the same conclusion with simple logic. Much nicer solution. Hurkyl, if you have a problem on the par with the ones posted so far, please post it. I would have trouble comming up with a good one.
     
  17. Sep 4, 2003 #16

    Hurkyl

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    Yep, Integral got the right answer, and Ahrkron got the clever solution!

    I don't have any other good ones off hand, though...
     
  18. Sep 4, 2003 #17

    chroot

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    As a Math Doctor on Drexel's "Ask Dr. Math" website, I see a whole lot of clever math puzzles come through the door. I will try to post some soon!

    - Warren
     
  19. Sep 4, 2003 #18

    marcus

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    referree call

    Hurkyl asked, Integral answered (seconded by Ahrkron)
    The turn goes to Integral, who passes back to Hurkyl
    and Hurkyl declines the turn.

    Therefore it is Ahrkron's turn. Ask a good one, Ahrkron!
    If you dont happen to come up with something subtle then
    ask something
    straightforward. This could be a good game.
     
  20. Sep 5, 2003 #19

    ahrkron

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    OK, here it is:

    You probably know the following riddle:


    John leaves home one morning and does the following:
    - Stands in front of his house, facing South
    - walks straight ahead for 1 mile,
    - turns left and walks 1 mile, sees a bear
    - turns left and walks 1 mile,
    at which point he finds himself back home.

    Riddle's question: What is the color of the bear?


    The solution (the color of the bear) is unique. My question is: if we take the bear out of the question, how many different ways can such a walk be achieved? explain!

    I will give some hints if necessary.
     
    Last edited: Sep 5, 2003
  21. Sep 5, 2003 #20

    Integral

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    Couple of things I would like to see.

    A derivation of some sort, or at least an indication of the logic used should be a part of the solution..... There may be some who are wondering how to get the solution to that first problem (think quadratic !)

    Also I see quality problems as important as who posts them. The winner gets first shot, but if he does not have a good proplem I would rather it be passed to someone who has one.
     
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