I need your help...its a puzzle

[Bunny13]

I was given this puzzle to solve and I am having some trouble with it so I thought I would throw it out to the fish keeping community so everyone can have a go at it! The object is to find the area of the dark blue sections of the oval. All the sections are evenly spaced.(There are a total of 4 evenly spaced sections, the horizontal dashes are in the middle of each space! Sorry about the drawing) There is no math involved nor do you need any numbers to figure it out. I was told that a child, who didn't know any math, would have an easier time figuring this puzzle out then someone who has extensive knowledge in the subject. I'm not very good at these kinds of puzzles! Any ideas? :huh:

http://i30.photobucket.com/albums/c303/Bunny1113/Windowproblem.jpg

[kveeti]

The object is to find the area of the dark blue sections of the oval.

My problem is, I don't understand the question. Does that mean what % or fraction the dark blue section is??? Also, I would like to know if the light blue section is on top of the dark, or does it displace it?

[UncaBret]

I found them! Theres one at the top and one at the bottom!

[Hannys_Papa]

Well i did the mathematical approach which is fairly quick and simple.

Known things:
Pi = 3.14
A(circle) = Pi*r(squared)
A(ellipse) = Pi*a*b
r = Radius of circle
a, b = halfaxis of the ellipse

A1 (light blue) = A(circle)
A2 (dark blue) = A(ellipse)

We call the area to be found A3. A3 = A2 - A1

A3 = Pi*a*b - (Pi*r(squared))

We know from the drawing that r = a and b = 2r
so

A3 = Pi*r*2r - (Pi*r(squared))
A3 = 2Pi*r(squared) - (Pi*r(squared))

A3 = Pi*r(squared)

EDIT: So the poster after me showed it even better (simpler?) that the dark blue area = the light blue area ;)

[mvigor]

A quick Google search told me

http://mathforum.org/library/drmath/view/55402.html

that the area of the outer elipse (oval), if it were complete, would be defined as pi * a * b. a = 1/2 the length of the long side of the elipse and b = 1/2 the length of the short side of the elipse.

In your image the long side is 4 and the short side is 2.

pi * (a/2) * (b/2) =
pi * (4/2) * (2/2) =
pi * 2 * 1 = 2 pi.


The area of the smaller, light colored circle can be calcuated at pi * radius^squared. The radius is half the diameter, or half of 2. The area of the inner circle is pi * 1^2, or simply pi.


Subtract the inner circle from the area of a complete ellipse and you'll know the area of the part that remains. 2pi - 1pi = pi.

The dark blue area is equal to the light blue area.

Please correct me if I'm way off here. I don't really love math. :)

[UncaBret]

I still think I was right. Remember, a child with no math skills can do it!

[TKOS]

I assume the answer is 2.

[Bunny13]

Does that mean what % or fraction the dark blue section is??? Also, I would like to know if the light blue section is on top of the dark, or does it displace it?


I dont think the problem has anything to do with math, no %s or fractions. The light blue section displaces the dark blue section.


I like UncaBret's answer and knowing the person who gave me the puzzle that sounds like an answer they would be looking for!

I :clap: those who could figure it out using math....not my strong point! I will find out later today what the answer is and I will be sure to let everyone know!!!!

Oh, TKOS, why 2?

[TKOS]

You need to find the area of the dark blue, there are 4 evenly spaced sections. So 2.

[joephys]

I agree with UncaBret. Would have never got that on my own.

[sumthin fishy]

the answer is 0. The light blue section gives the impression that the other part is dark blue, but its just plain old blue. there is no part that is dark blue.

[rosita]

I found them! Theres one at the top and one at the bottom!

Hurray!!! Someone else that thinks like I do!! Thanks UncaBret, I needed the boost!!http://bestsmileys.com/signs5/12.gif

[Watcher74]

I think the entire idea of finding a difference between "light" blue and "dark" blue egocentric and demeaning to blues of all shades.

Why can't we focus the similarities instead of pointing out the differences?

[joephys]

Bunny never told us what the answer was.

Well, the most important shade of blue is the hoovaloo. (I proabably spelled that wrong, but it doesn't matter, if you know what it is, you know what I mean.)