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Forum
-> The Social Scene
-> Games
miriam
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Wed, Aug 30 2006, 4:55 pm
Here is a graphical riddle for you guys.
If you solve it, post here and say so, then PM me with answer, and I'll reply if you got it right. But don't give away the answer here.
(Click on it to see it full size.)
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ny21
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Wed, Aug 30 2006, 5:09 pm
sorry ! cant answer ! I am no rocket scientist !
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Crayon210
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Fri, May 02 2008, 2:28 pm
Reviving this for you logic puzzle girls.
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Tamiri
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Sat, May 03 2008, 10:56 am
Does it have to do with displacement due to angles?
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grin
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Sat, May 03 2008, 12:32 pm
hint: compare the pieces in each diagram.
(no, I'm not a rocket scientist, either. just have an eye for detail.)
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miriam
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Sat, May 03 2008, 8:21 pm
Just a reminder, the pieces are identical in each figure.
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GAMZu
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Sat, May 03 2008, 8:34 pm
Tamiri is right, and I figured it out, but it does not have a one "aha!" answer. It kid of involves an explanation.
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Tamiri
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Sat, May 03 2008, 10:40 pm
So, Gamzu, please explain! I am thinking that the angle at the top of the triangle changed so that affects everything but I would like proper proof and I am no mathemetician to be able to do it myself.
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grin
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Sat, May 03 2008, 10:54 pm
miriam wrote: | Just a reminder, the pieces are identical in each figure. |
I protest - if you look carefully, one is not!!
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Tamiri
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Sat, May 03 2008, 10:57 pm
The puzzle itself states that the partitions are all the same in both figures.
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Mrs. XYZ
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Sat, May 03 2008, 11:00 pm
I see where the "extra' is, but cant explain it.
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GAMZu
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Sat, May 03 2008, 11:04 pm
grin wrote: | miriam wrote: | Just a reminder, the pieces are identical in each figure. |
I protest - if you look carefully, one is not!! |
How?
One triangle is 2x5 squares and the other is 3x8. Same in both figures.
The other shapes are also obviously the same.
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grin
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Sat, May 03 2008, 11:08 pm
count the sq. in the red shape
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grin
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Sat, May 03 2008, 11:40 pm
you're right; I miscounted. and I give up - what's the answer?
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leomom
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Sat, May 03 2008, 11:41 pm
If you look closely at the top figure, you can see that the "hypotenuse" of the large "triangle" (made up of all the parts) is not actually a straight line. The two hypotenuses (hypoteni?) of the green and red triangles do not quite line up.
So, if you follow the "line" of the top down from the top right to bottom left, and compare that to the same line in the bottom figure, you'll see that the one on the top is slightly higher in each box...
stopping here as I'm not sure I was supposed to actually say anything... but I do want to point out that I just noticed this while looking at it now for the first time and I've never seen this puzzle before.
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Mrs. XYZ
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Sat, May 03 2008, 11:48 pm
YY, I realized that too, but how do you explain it?
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grin
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Sat, May 03 2008, 11:54 pm
I think that means that IRL all the shapes either wouldn't quite fit together or would have rounded sides.
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leomom
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Sun, May 04 2008, 12:03 am
Well, the angles are only at the top. Everything that has to fit together is made up of right angles, horizontal/vertical lines. So when the pieces are stacked differently and the position of the two triangles switched, they can still fit together, but there is a bit of "breathing room" that opens up (which is made up of the bits of the triangles that end up higher in the diagram on the bottom).
If you want to make it more obvious, try drawing the same thing on a piece of graph paper, but really exaggerate the difference between the angle of the hypotenuse of the red and green triangles. Make it so that the overall shape doesn't look like a right triangle, but instead either has a bump on top or a big dip... you'll see what I mean if you try it...
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GAMZu
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Sun, May 04 2008, 12:49 am
OK, since the answer is coming out, I'll add my 2 cents.
The 2 triangles aren't proportional to each other. Their slopes are similar, but not identical. The top figure's slope is concave, bending in.
The bottom figure's slope is convex, arching out. Neither shape has a straight slope.
So since it bends out, there becomes a void inside. Hence the empty square.
In order for the shapes to be rearranged without the extra box, the 2 triangles should have had the same proportions.
Not 2/5 and 3/8 but
either 2/5 and 4/10
or 1.5/4 and 3/8 ...or anything of the sort.
Then their hypotenuses (slopes) would be identical, like yy said. And there would be no extra square.
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