This is tough... your brain may explode!!!

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Posted by zzleeper on Feb-01-2002 06:34:

This is tough... your brain may explode!!!

This is the link:

http://www.click2amuse.com/fun/optical/opt.php?ID=37

Who will be the one to answer this one??? It has occupied the minds of every genius in the last 80 years since Bertrand Russel discovered it in 1931.

BTW if u can�t answer it, i will only post the answer if this post has 100+ views..

HOPE U LIKE IT!!!

Posted by zzleeper on Feb-01-2002 06:44:

C�mon guys!!! U re intelligent

Answer it!!!

Posted by LoopStyle on Feb-01-2002 07:09:

cuz the green block has room for 2 orange blocks. it's all on size of blocks. well I tryed

Posted by Fundamental on Feb-01-2002 08:46:

Ooh. That's a real bitch. The gradient has gotta be slightly different or something, coz a similar 8x2 rectangle can't fit into the first triangle if you look at the picture closely.

Posted by Pjotr G on Feb-01-2002 08:52:

u can use the quares (and your ability to count) to see that the figures are the same....and that there is the same slope! I don't get it!

Posted by Cosmo on Feb-01-2002 11:26:

Ha-ha-ha! Real tricky! But i know the answer!
zzleeper Check PM box

Posted by DjChook on Feb-01-2002 12:46:

Damn i once knew that ...

Forgot it now although...

Posted by Pjotr G on Feb-01-2002 13:05:

wait a minute...the slope IS in fact different....

5:2 is not the same relative as 8:3

when you translate 5:2 it becomes 7.5:3

AHAAA hope I haven't spoiled anyways fun lol

Posted by zzleeper on Feb-01-2002 13:42:

Well IT IS about slopes... uhm okey Pjotr G u had the answer... more or less...

**DONT READ THIS IF U STILL WANNA FIND OUT BY YOUR OWN**

The gradient of the combined figure is 5/13 = 0.3846

So the real height of the red triangle would be 8*0.3846 = 3.07

And the real height of the greenish�? triangle is 5*0.3846= 1.92

So if u check well u find out that the "rectangles" in the two pictures are of different height...

But doing it graphically would be difficult cos its a distance so small u would find out (the borders would make it less obvious)...

It was a good challenge for me.. hope it u like it...

Ps: Cosmo, what is "PS"???
If anyone wants to know mail me or post it here.. i ll answer when i get back from the carl cox rave... uhhh how is carl cox dj�ing this days??

Posted by inatrance on Feb-01-2002 14:27:

hahahaha got it! before I read all the other posts, made me think for a while

Posted by {b.s.e.} on Feb-01-2002 18:32:

shite. not 61 views.

the slope is different.
i don't really understand the question, though. so what if the pieces can be arranged to form an imperfect triangle? how is that impossible?
i don't really know what i am answering..

Posted by nomatteus on Feb-01-2002 23:25:

not even 100 views and you already posted the answer...

Posted by zzleeper on Feb-02-2002 20:40:

I ve just returned to town.. so uhm i thought it would be kinda mean to leave you w/out an answer for too much time (at least if u re like me, kinda impatient..)..

Oh.. one last thing b4re this thread gets closed :O... Cosmo, do u have more of this type of quizzes\stuff .. ????? Post Them!!!

Posted by Cosmo on Feb-02-2002 21:53:

quote:
Originally posted by zzleeper
I ve just returned to town.. so uhm i thought it would be kinda mean to leave you w/out an answer for too much time (at least if u re like me, kinda impatient..)..

Oh.. one last thing b4re this thread gets closed :O... Cosmo, do u have more of this type of quizzes\stuff .. ????? Post Them!!!

I've got megatonns of them!
Watch this space!

Posted by Bondor on Feb-03-2002 05:45:

way easy

the hypotinuse of the first triangle is is not a staight line you all are stupid

easy

Posted by zzleeper on Feb-03-2002 06:18:

Well u re COMPLETELY OUT OF BASE Bondor.. the answer does not relate to that.. in this puzzle the problem lies in the graphic but not in the shape of the hypothenusa, but in the difference of height of the rectangles. The area of the triangles is the same in both graphics (well at least in my solution):

Posted by AnotherWay83 on Feb-03-2002 18:52:

u guys are all wrong lol...sumtime back at rmf the same topic came up...i have provided an explanation of the answer there...just read my posts and follow the links i've posted, thou shalt be enlightened in no time...and i know this is the answer, 100% sure of it..

http://www.raremusicfinder.com/foru...&threadid=16026

peace

Posted by zzleeper on Feb-03-2002 22:00:

THE REAL REAL REAL ANSWER

Hi everybody.. well it seems that there has been some confusion about the answer to this post. Well as I want to set this straight i�m gonna try to answer this in the best possible and easy-to-understand way.

Disclaimer: Even if I believe I�m right I may be.. wrong.. but the chance is very small so...

Well here we go. First of all, I have to sadly say that even AnotherWay83 is wrong. Everybody is

The interrogant in this quiz is the fact that if we rearrange the parts of a triangle that has an area of 32.5 u�(where u is an imaginary unit, it could be inches, centimeters) in a specific way, then there is a space missing. That would mean that the area of the total triangle has been reduced even if the area of the parts have not. Well there is something bad about that, if not then my 11 years of math at school would have been worthless.

The solution is this: (posted before but without good explanation)
Both triangles have the same slope (note: forget about the milesimal error in the graphic, that was a mistake in the drawing) which is 0.3846. The small triangle has a height of 1.92u�, NOT 2u�. The height of the large triangle has a height of 3.07 u�, NOT 3 u�. This are the formulas:

LENGHT * SLOPE = HEIGHT
8 * 0.3846 = 3.07
5 * 0.3846 = 1.92

But in BOTH graphics, the red and green triangles are the same, and THE AREA THE TRIANGLES OCUPPY IS THE SAME. The answer lies in the RECTANGLES, that most people forget to analyze:

In the first graph the height of each square is 3.07/3 = 1.02
In the second one the height of the squares under the red triangle is 1.92/2 = 0.96

There are 15 "squares" (well now that we know they arent really squares) in the 1st graph and 16 in the second (counting the blank one)

And the area of the 15 squares of the 1st graph is the same as the area of the 16 squares of the other graph because:

1*1.02*15 = 1*0.96*16 = 15.38

So the FINAL FINAL REASON OF THIS OPTICAL ILUSION LIES IN THE FACT THAT THE YELLOW SORT_OF_RECTANGLE and THE GREENISH SORT_OF_RECTANGLE (SORRY I DONT KNOW THE NAME IN ENGLISH FOR THAT SORT OF FIGURES) DONT HAVE THE SAME AREA IN BOTH GRAPHS!!!!!!!!!!!!!

But, why haven�t we noticed?? Because the difference of height is SO small that we can�t perceive it correctly. The only graphical difference we CAN perceive is the hypothenusa that ironically is only a mistake of the creator.

So, this is the end of my VERY SHORT post. Remember: The area of the first graph equals the area of the second one PLUS the blank space. The green and red triangles have the same area. The slope is the same.

Any hate mail please forward to my math teacher for being such a masochist enslaver.. LOL LOL

Posted by AnotherWay83 on Feb-03-2002 23:25:

i read my solution in math books and even math forums, im pretty sure im rite...ithink u're also rite..we're saying the same thing i think

peace

Posted by zzleeper on Feb-03-2002 23:41:

Possibly

Well u might be right about that we are both right.

Maybe it can be explained in both ways. But the thing I can�t understand is how exactly the answer u wrote explained the blank space..

I think now i m gonna try to forward the question to my college math teachers and try to fux0r with their minds. Hopefully they�ll go nuts..

Bye..

Ps: If u see around any interesting puzzle like this post it in this forum

Posted by AnotherWay83 on Feb-04-2002 00:50:

becuase as bondor said the hypotenuse is bent outwards...

peace

Posted by zzleeper on Feb-04-2002 02:06:

quote:
Originally posted by AnotherWay83
as bondor said the hypotenuse is bent outwards...

Does that IMPLIES that there should be a blank square?

Piz

Posted by AnotherWay83 on Feb-04-2002 03:44:

quote:
Originally posted by zzleeper

Does that IMPLIES that there should be a blank square?

Piz

yes it does...the areas of all the individual elements have not been changed...so the sum total of the areas stays the same...

peace

Posted by Cosmo on Feb-04-2002 17:23:

quote:
Originally posted by Bondor
the hypotinuse of the first triangle is is not a staight line you all are stupid
easy

1.If ANY side of the triangle is not a straight line its not a triangle! (Well, unless it's drawn on a ball, or any other not_flat surfuce)
2.Hypotinuse is a side of the triangle, it's cannot be "not straight"!
So, what u said about "stupid"?

quote:
Oroginally posted by zzleeper
in this puzzle the problem lies in the graphic but not in the shape of the hypothenusa

Wrong! But...hmmm...probably, this is becouse our basic assumptions are different. Me, and others (sorry, I don't say who exactly ) consider all measurements of all small parts and all squares to be integer, thus the reason of difference in two figures is it's "hipotinuse" - it's not straight, becouse tans (or slope, how u call it) of smaller angles in triangles are different. While u consider it to be straight, and measurements are not integer.

So, becouse the pic has no exact description, we have to depend only on our sight.
And here comes analysis of the pic!
If you won't see it here it's wether you are blind or it's just sometning about me :
1.Here's the analysis of the slope:

(small grey lines at the ends of "hipotinuse" are equil, Iv'e just copied and pasted them)
2.Here's the analysis of the figures' height - it's completely equil:

So, let me continue on my solution.
Lets see... The area of the figure (not triangle! In reality it's [u]quadrangle[u] ) that consists of:
Red tri.+dark green tri.+yellow/light green rectangle= 0.5*3*8+0.5*2*5+3*5=32
If this figure would be triangle it's area would be? Correct! : 0.5*13*5=32.5
On upper figure we have -0.5 from area of the triangle
On lower figure we have +0.5 from area of the triangle
But becouse both figures consist of the same parts we have (0.5+0.5)=extra square.

Posted by zzleeper on Feb-04-2002 18:04:

Well I finally understand exactly your answer. One funny thing is that we re both right in how can we explain the empty space with the overall figure of the same height and lenght. But my assumption was that the rectangles changed its height by millimeters, and yours (which i guess it fits better the graphic) that the triangles were the ones that changed... but anyway i�m impressed by everyone�s skill to resolve this problem :O

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