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Math Help - A classic riddle

  1. #1
    dud
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    A classic riddle

    This little riddle is written by the Indian mathematician Bhaskara(1114-1185), in his book Lilivati.
    Originally he wrote it to give his keep his daughter occupied with(rather than an unhealthy love-affair)

    Out of a flock of geese, ten times the square-root [of the total] went to the Manasa lake when a cloud approached,
    one-eighth went to a forest filled with hibiscus,
    and three couples were seen playing in the water.
    Tell me, maiden, the number of the flock.


    It's not perhaps the hardest riddle, but it's a neat one. Also you can easily get stuck if you don't read it correctly, or if you try to think overly-complex!

    PS: Don't spoil the fun for everyone else by blurting out the answer. If none has understood it in a week or so, I'll post an explanation
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  2. #2
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    Tricky,

    I keep getting fractions of geese
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  3. #3
    dud
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    Hehe, as I said... It looks easy, but somehow you end up crunching at it for a while!
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  4. #4
    dud
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    The solution!

    I suppose it's pretty safe to post the solution now, as it seems the (little interest that was) has died out

    The correct representation of this word-puzzle in mathematics terms follows.
    By making x be the number of total geese on the left side, and then putting in the word puzzle on the right we get this:
    <br />
x = 10\sqrt{x} + \frac{1}{8}x + 6<br />
    Lets do the maths then...
    <br />
10\sqrt{x} = x - \frac{x}{8} - 6<br />
    <br />
10\sqrt{x} = \frac{7x}{8} - 6<br />
    <br />
(10\sqrt{x})^2 = (\frac{7x}{8} - 6)^2<br />
    <br />
100x = \frac{49}{64}x2 - 10 \frac{1}{2}x + 36<br />
    <br />
\frac{49}{64}x2 - 110 \frac{1}{2}x + 36 = 0<br />
    <br />
x = 144<br />
    144 geese in total

    There are two little tricks to this riddle.
    Remember that on line 3 you have to use the correct expansion.
    On line 5 you have to treat it like any other second degree polynominal.
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