A Really Simple Puzzle

[Thetyim]

[bino]

I can see it right away.

The red triangle is 8 blocks long, dark green one 5, giving you an odd number.

The brown and light green shapes are 5 blocks long when stacked, and 8 blocks long placed side by side.

The fact that the "middle row" of the shape blocks in the original configuration is not divided equally (2,3 blocks - odd number) would make it impossible for them to fit together equally side by side.

Edited May 2, 2005 by bino

[Thetyim]

Sorry Bino, didn't understand your explanation.

By brain must be ill today.

How come the same four shapes take up less area in the lower arrangement.

[doctormann]

The perimeter of either figure is not, in fact, quite a triangle.

If you get your calculator out and compute the angles of the red and green triangles (do the inverse tangent) you will find that they are not the same. Therefore the 'hypoteneuse' of either of the perimeter figures cannot be a straight line.

The fact that both figures look as though they should occupy the same overall area is, therefore, a bit of an illusion. The sums of the areas of the component parts do, of course, occupy identical areas - it's just the overall area that is different.

Clear as mud, I expect, but maybe it helps. You could always cut the figures out of paper to convince yourself.

DM

[Khutan]

The total area of both triangles is the same, just the perimeter of the first (red) triangle is larger. The difference being made witth the extra-odd square.

Counting the "area under the curve" will show this.

[BrissyBoy]

It is an optical illusion.

The top triangle bows in(concave).

Whilst the triangle at the bottom bows out(convex)

Now because the red triangle is larger than the green one because they bow then the area changes in a way that leaves a small space.

Thy this: Make it yourself using graph paper with straight lines and you will get quite a different result. It should not have a space.

Sorry if i have ruined this for anyone.

Edited May 2, 2005 by BrissyBoy

[bino]

I'm begging to differ....

Granted that the image is an optical illusion, and the triangles have different angles.

However, neither hypotenuse really matters as they do not cross or make up the space that becomes the hole. The only parts of the triangles that matter in the second image are the base of the larger red triangle (8 blocks) and the vertical of the dark green triangle (2 blocks).

Tough to explain, and a picture is worth 1000 words. I've added blue and purple colors to the image with photoshop to demonstrate my explanation.

Simple really!

Sorry to everyone- you need to click the link to see the image. I tried to figure out how to make this image visible and couldn't do it. Can someone tell me?

Edited May 2, 2005 by bino

[peder.klockmann]

LMAO, I think it might help you out if you print it... and cut all the pieces out. Maybe then you'll understand.

1. Print

2. Cut out the triangle without the space

3. Cut all the pieces of triangle one into their corresponding shapes

4. Place all of the shaped onto the triangle with the space

If, it is an optical illusion; Then how the F* do they all fit into place MR. BrissyBoy?

Edited May 2, 2005 by peder.klockmann

[BrissyBoy]

Sorry Peder i think i own you an apology.

Looking at it on the screen it seemed that it was curved and that was my reasoning.

Good fun but?

[peder.klockmann]

Sorry Peder i think i own you an apology.

Looking at it on the screen it seemed that it was curved and that was my reasoning. 

Good fun but? 

<{POST_SNAPBACK}>

You don't owe me an apology, I think I might owe you one for singling you out dude. Sorry, heheh.

[siamesekitty]

I've seen this one before, have heard it explained... BrissyBoy is right. Take a close look at the slopes of the triangles. One slightly curves inwards, the other slightly outwards. The resulting difference in the areas equals the area of the missing square.

[peder.klockmann]

Well then, maybe my printer, scisors, and paper are all in on this little hoax.

[bino]

Well then, maybe my printer, scisors, and paper are all in on this little hoax.

Mine too!

Maybe we didn't shave off the differences between the triangles and make them fit in the hole?

[peder.klockmann]

Right now I'm busy proving that all shapes are exactly equal on both top in bottom in CAD, wow I guess I'm that bored and have nothing else better to do at work.

[linlin]

I have seen the same problem when I was taking online IQ tests. Here you go, the solution is also there.

http://www.highiqsociety.org/common/puzzles/puzzle03.htm

[peder.klockmann]

Here is what I came up with, I used Viso instead. If anyone wants me to email them the .vso file let me know and I will be happy to.

[LivinLOS]

Without wanting to make it all to technical its simply down to the innaccuracy (or thickness) of the triangle lines making up the problem..

Look at the two triangles.. One is a slope of 5/2 and the other is a slope of 8/3 so obviously you are not dealing with equally angles on the slopes.. By using a slightly fat black line also helps to mask this effect...

[Thetyim]

Thanks Peder and Livinlos

I understand now.

[Boh Bpen Yang]

You really don't even need a cut out or a calculator to see that it is an optical illusion. It's layed out on a graph. Look a the intersection points on the graph #1 and compare to graph #2. They are not the same.