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Dave W.
Info Junkie
USA
26020 Posts |
 Posted - 03/30/2005 : 21:51:15 [Permalink]
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quote:
Originally posted by dv82matt
This one baffles me though. Does anyone have an explanation?
Yes. Do you want to hear it? |
- Dave W. (Private Msg, EMail)
Evidently, I rock!
Why not question something for a change?
Visit Dave's Psoriasis Info, too. |
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beskeptigal
SFN Die Hard
USA
3834 Posts |
Posted - 03/31/2005 : 00:24:29 [Permalink]
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quote:
Originally posted by Dave W.
quote:
Originally posted by dv82matt
This one baffles me though. Does anyone have an explanation?
Yes. Do you want to hear it?
I do, though I know I have seen the answer before and can't remember it. |
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dv82matt
SFN Regular
760 Posts |
Posted - 03/31/2005 : 00:50:51 [Permalink]
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quote:
Originally posted by Dave W.
quote:
Originally posted by dv82matt
This one baffles me though. Does anyone have an explanation?
Yes. Do you want to hear it?
Please, do tell. |
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Dave W.
Info Junkie
USA
26020 Posts |
Posted - 03/31/2005 : 07:09:34 [Permalink]
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| Okay, okay. The black lines in the figure hide the fudges. You'll note that for the yellow and green triangles, the slope of the diagonal side is 3/8, or 0.375, while the slope of the diagonal side of the blue and red parallelograms is 2/5, or 0.4, so they don't match up. In the 5x13 figure, the thickness of the black lines hides an extremely thin parallelogram running diagonally from the upper-left corner to the lower-right corner. If you do the math, you'll find that the area of that hidden parallelogram is... one. |
- Dave W. (Private Msg, EMail)
Evidently, I rock!
Why not question something for a change?
Visit Dave's Psoriasis Info, too. |
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beskeptigal
SFN Die Hard
USA
3834 Posts |
Posted - 03/31/2005 : 11:40:10 [Permalink]
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Oh! They cheated again.
But I have a question. The triangles are on the same grid. So does the grid differ from side to side? Or do the triangles just not really match which is what I think you are saying? |
| Edited by - beskeptigal on 03/31/2005 11:44:02 |
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Dave W.
Info Junkie
USA
26020 Posts |
Posted - 03/31/2005 : 13:04:49 [Permalink]
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The triangles don't match up, beskeptigal.
In the figure on the right, the left side of the green triangle is 5 units in from the left tip of the yellow triangle. Using the similarity of triangles, we know the yellow triangle is (3/8)x5 units in its vertical dimension at that point, or 1.875 units. However, we know from the left figure that the left edge of that green triangle (in the right figure) should be 3 units high, making a total height of 4.875 units, when the right-hand figure is clearly labeled as being 5 units high. There is one-eighth of a unit "extra" in the figure at that point which would show up easily if the black lines were thinner or non-existant.
Actually, the slope of all the diagonal edges in the right-hand figure is 5/13, or 0.385, which is real close to 0.375 (the left-side yellow and green triangles) and a little less close to 0.4 (the left-side red and blue parallelograms), but in between both.
It's a cheat, yes, but the puzzle is asking you to find and explain that cheat.
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- Dave W. (Private Msg, EMail)
Evidently, I rock!
Why not question something for a change?
Visit Dave's Psoriasis Info, too. |
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dv82matt
SFN Regular
760 Posts |
Posted - 03/31/2005 : 21:23:50 [Permalink]
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quote:
Originally posted by Dave W.
Okay, okay. The black lines in the figure hide the fudges. You'll note that for the yellow and green triangles, the slope of the diagonal side is 3/8, or 0.375, while the slope of the diagonal side of the blue and red parallelograms is 2/5, or 0.4, so they don't match up. In the 5x13 figure, the thickness of the black lines hides an extremely thin parallelogram running diagonally from the upper-left corner to the lower-right corner. If you do the math, you'll find that the area of that hidden parallelogram is... one.
Thanks for the explanation Dave. That makes sense. |
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