i'm not thick... but i'm obviously not that bright either - was sent this and can't do it (grrrrr - don't you hate that?)

i even MADE the bloomin' thing and still don't understand. so if you're bored and know the answer, please save my sanity!

have a look:

http://www.unoriginal.co.uk/optical_illusions/illusions5_8.gif

so! y'all can't do it either!

You know, there's no true satisfaction if somebody else tells you the solution :P So I am not going to spoil you all the fun :) Unless you really want me to...

i'm the type of person that is satisfied when i know. and only then. explain it, and if i understand i will be satisfied.

EXPLAIN IT EXPLAIN IT EXPLAIN IT!

(please)

I keep thinking I understand it...and then...my mind just goes again. I understand on some level

R? where R you?

sue, i have NO level of understanding on this one, so just in case R doesn't come back (maybe he/she was bluffing) just get ready to get yourself back on here when the explanation resurfaces!

the thing is - I'VE MADE THE THING! IT'S REAL! but if you remember working out areas and stuff in maths, it just doesn't make sense. how CAN the shape have the same outline but different surface areas just because of how it's arranged. does noone out there do maths for a living?

Sorry, I've been out. Not bluffing ;p

Here the spoiler begins. If you want to guess yourselves, do not read further.

So, what we THINK we can see, are two large triangles. But IN REALITY none of them is the real triangle. The hypotenuse side of the upper one is concave, whereas the second one has the hypotenuse side convex. So these aren't really straight lines but curves. The tiny space between these curves is where you loose the additional square.

You can check it by comparing the angles in small triangles (the red and the green). If you e.g. calculate some trygonometric function of one of the angles (of course not the right one), you will see that these triangles are not congruent and therefore cannot form the large triangle as it is shown in the picture.

Hope, it wasn't too complicated (I still got some problems with expressing mathematical ideas in English ;p).

And btw, it's 'he'

Very clever. I first didn't believe, so I took the image to Photoshop and rotated the triangles over straight lines. Curve and convex then appeared clearly

Thank-you (mr.)R! can sleep peacefully again - i knew i would find someone to help on here. i'll still need to prove it to myself though, so over to photoshop i go...

Hi Insomniac, saw your puzzle and just had to try and find another solution without photoshopping. Well here goes. The area of the rectangle formed by the yellow and green shapes in the upper triangle is 15 square units(3 x 5). In the lower triangle it would have to be 16 square units (2 x 8) if the empty square was filled hence the missing section. Now I can sleep:)!!

Hope my solution below is clear enough. It's all to do with the total area covered by the two shapes IMHO. 15 squares in both cases.

hi boni - thanks for that. because the large rectngles both looked to be covering the same area, i just couldn't see where the extra unit could possibly come from. anyway, there's a rational explanation for (nearly!) everything

Then I have got one more - find explanation for that one :

Two friends are meeting after a long time. During the talk one of them asks:
- Do you have any children?
- Yes, I have got three - the other answers.
- How old are they?
- The product of their ages is 36.
- Then I don't know...
- The sum of their ages is equal to the number of trees outside.
- I still do not know.
- The oldest has blue eyes.
- Oh! Now I know!!

Now you tell me - how old are they?

P.S. It is pretty easy puzzle, although at the beginning it may seem ludicrous.

***spoiler***

hm... if you'd said that the youngest has blue eyes, i think i might have the solution, it would be that they are 6, 3, and 2. but like this i don't quite see why it can't be 9, 2 and 2, or 4, 3 and 3.

***end of spoiler***

anyone else?

@shani:
There is only one correct answer to that problem