I just saw this over on io9, and thought it was pretty cool. No, don't go looking. See if you can figure out what happened to the "missing square". Obviously it would be polite if any speculation is "spoiler-colored" or in super small text, for those who don't know but want to figure it out on their own.

I've seen this ancient riddle too many times to count, so I won't give it away.

And I thought I was relatively "up" on math riddles...

ME too :/

I actually just noticed now, by zooming in on a few certain lines in those triangles varying slopes between those top two triangles really cuts out a square, doesn't it?

The blue section of the second triangle has an extra square. It is a bit longer than the section on the first triangle.

Am I correct?

DShiznit brought me over here.

My input: http://pastebin.com/raw.php?i=nC5CstiD

AmIrite?

The angles for the red and blue triangles are slightly different
I think I'm correct.

I am so confused. If I calculate the area of the top triangle, L * W / 2, or 13 * 5 / 2, I get 32.5 sq units. But if I calculate each peace individually, 12, 5, 7, and 8, and then add them up, I get 32 sq units. If I calculate the area of the bottom configuration, but first doing L * W /2, and then subtract 1 sq unit for the one square it doesn't cover, I get only 31.5 sq units. This defies everything I learned in 5th-grade geometry!

EDIT- OHHHH I GET IT NOW. Souvik and Ashbad were right. the slope of the red triangle is 3/8, the slope of the blue triangle is 2/5, they aren't similar and thus aren't actually forming a triangle when combined! What we were assuming are 2 large triangles are actually a quadrilateral and a heptagon, and thus all the rules we've been using actually don't apply!

Hint - they have the exact same surface area; nothing from the first one got lost.

There. I think I got it. The slope of the red triangle is 3/8 (0.375) and the slope of the blue triangle is 2/5 (0.4). If you take the area of a right triangle with a base of 13 and a height of 5, you get 32.5. If you add up the areas of all the shapes, you get 32. In the first shape, the junction of the two triangles are slightly concave, due to the smaller slope coming before the larger. In the second shape, the junction is convex due to the larger slope coming before the smaller slope. Once you realize this, you can easily pick it out from the diagrams. Pretty cool, eh? Just copy this entire phrase in to a simple text editor.

All of the components are the same size between top and bottom.




You have it exactly right and did a good job with the explanation, except maybe your definition of WYSIWYG With your post....what we see is not what we get, unless we use a plain-text editor.



I'm glad this got some of you thinking hard, and that several of you have produced correct answers!

Elfprince13, I agree that mathematical riddles are always fun and a good way to get the brain working; do you have any other ones for us? Actually, come to think of it, I have this one that we puzzled over for many minutes on IRC. Shaun was the first to get it, to his credit.

0000 = 4
5749 = 2
5555 = 0
2048 = 4
3084 = 4
1234 = 1
8088 = 7
1111 = 0
9999 = 4
7685 = 3
6311 = 1
8456 = ?

This is a fascinating puzzle. Nothing is immediately obvious to me after a few minutes of looking at it, which, I guess, is why it's a riddle.


And I don't have any more math riddles off the top of my head, but I'm sure I'll remember one or two.

I have lost all hope of what I see is what I get.

I looked at this puzzle this morning for a few minutes but didn't figure it out. Then I figured it out in a few seconds this evening.
8456 = 4
Amirite?

I spent longer than I needed to on this. Here is the answer I got and the process I went through.

I realized at the end that it was much simpler than I made it. :)

This isn't quite a riddle, but it's freaking awesome and kind of like one: http://math.univ-lyon1.fr/~borrelli/Hevea/Presse/index-en.html Mathematicians finally figured out how to construct a torus from a plane without length-distortion. It looks approximately like this and falls in between normal geometries and classical fractals:

I have too, and it tricked me so badly at one time, but when I got it, people would beg me for the answer. No hints from me

I know this one, and yes!

I like the clever way of hiding your solution, but this forum needs spoiler boxes!