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Can anyone figure this out? (non-GCing topic...tread carefully)


pizzachef
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I reckon there's a buncha smart people here. Has anyone seen this and figured it out?

 

Yes I admit, I'm an engineer and this goofy little puzzle stumps me...flame all you want [:D].

 

Click here for the puzzle.

 

Sorry about the link not working...friggin geocities.

Try to paste this URL into the address bar up there:

 

www.geocities.com/geoffreyforest/puzzling.jpg

 

I think for it to work right...you have to physically paste or type the address in.

 

[This message was edited by pizzachef on August 14, 2002 at 11:40 AM.]

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To expand on what gromit said: The overall shapes are not really triangles. The "hypotenuse" on the top shape bends inwards while the on one the bottom bends outward. the difference is slight.

 

____________________________

The true traveler is he who goes on foot, and even then, he sits down a lot of the time.

- Colette

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try drawing the shape on graph paper...with STRAIGHT edges..it comes out the same.

 

What I did was look at the areas...the areas of 2 triangles and the two odd shapes.

 

The area of all the shapes added together is 32. Even with the one with the hole...the area of the shaded shapes is still 32, but add the hole in and you get 33!

 

Even more wierd...the area of the entire big triangle is 32.5!!!!

icon_eek.gif

 

-pizzachef

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If by "straight" you mean you drew a straight line between the upper right and lower left corners of the overall shape. Then look carefully at your drawing. The 'midpoint' of the hypotenuse (where the two smaller triangles meet) will not cross directly over the coordinates on your graph paper. If it does, try using a thinner pencil.

 

- OR -

 

Redraw the picture with larger (but proportional shapes) (i.e instead of the smaller triangle being 5 x 2 make it 25 x 10.

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If you look closely at the two small triangles, you will see that their angles are not the same; the blue one has a slope of 3/8, or 15/40; the red has 2/5, or 16/40. As such, they do not form a straight edge for the hypotenuse of the complete triangle. The top shape actually bows inward where the blue and red meet, the bottom bows outward.

 

With that in mind, imagine a line from the tip of each of the conglomerate triangles, the *true* hypotenuse. The area of this triangle is:

A = .5*13*5 = 32.5

 

Now, subtract from that the area of the individual small shapes (in the top "triangle"), and you get the area of the triangle formed by the real hypotenuse and that of the two small triangles in the top shape (empty space)

A = 32.5-7-8-(.5*5*2)-(.5*3*8) = 0.5

 

Double that value, since an equal amount bulges out of the bottom shape, and there is your missing 1.0 unit.

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The angles of the green and red triangles are slightly different. It's an illusion that together they form a straight line. Start at the top right of each shape and go left 5 and down 2. On the top one, you'll end up right on a grid intersection but not on the bottom one. That's proof that the two triangles have different angles.

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Look at the point where the red and green triangles meet in the first figure. Call it point D. Now look for point D in the second figure. You will see it is slightly inside the red triangle. Now draw a line from point D to the top point of the red triangle. Draw a second line from point D to the left most point of the green triangle. If you cut along these two lines, you will have a long slender sliver, whose volume is the save as the little square gap at the bottom.

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the slopes are so close, nonetheless, they're not equal. 2/5 is NOT 3/8

 

WHen I tried cutting otu the shapes and doing it by hand, I guess I assumed the mismatch was my error. That's what happens when we assume icon_rolleyes.gif

 

Thanks for the help! Everyone can now rest assured that I'll NEVER make that mistake when I'm designing a bridge that you might cross one day icon_biggrin.gif

 

-pizzachef

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