# A classic riddle

• Jan 12th 2006, 02:02 PM
dud
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 ;)
• Jan 12th 2006, 02:34 PM
MathGuru
Tricky,

I keep getting fractions of geese ;)
• Jan 12th 2006, 02:49 PM
dud
Hehe, as I said... It looks easy, but somehow you end up crunching at it for a while! :D
• Jan 24th 2006, 12:46 PM
dud
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:
$\displaystyle x = 10\sqrt{x} + \frac{1}{8}x + 6$
Lets do the maths then...
$\displaystyle 10\sqrt{x} = x - \frac{x}{8} - 6$
$\displaystyle 10\sqrt{x} = \frac{7x}{8} - 6$
$\displaystyle (10\sqrt{x})^2 = (\frac{7x}{8} - 6)^2$
$\displaystyle 100x = \frac{49}{64}x2 - 10 \frac{1}{2}x + 36$
$\displaystyle \frac{49}{64}x2 - 110 \frac{1}{2}x + 36 = 0$
$\displaystyle x = 144$
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.