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Subject: Geometry problem
Posted by: weykool
- [2842717] Wed, Apr 15, 2009, 14:45
Couldnt sleep last night and was watching Poker After Dark.
Chris Ferguson posed the following question:
You have a pyramid with a 1x1 base and equalateral triangles for the sides.
You have a tetrahedron again with with equalateral triangles that are the same area as the triangles on the pyramid.
(For those of you who dont remember a tetrahedron is a 3 sided pyramid)
Put both shapes next to each other so the bases line up.
Now tilt the top of the tetrahedron over until the apex of both shapes are touching each other.
The pyramid has 5 sides while the tetrahedron has 4 sides.
When the two shapes are joined together how many sides will the new shape have? |
| 1 | Guru
ID: 330592710
Wed, Apr 15, 2009, 17:09
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7, I presume.
One side of each disappears.
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| 2 | weykool
ID: 2842717
Wed, Apr 15, 2009, 17:31
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7, I presume.
One side of each disappears.
Incorrect.
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| 3 | Guru
ID: 330592710
Wed, Apr 15, 2009, 18:22
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Then it must be 5.
Hard to imagine based on intuition only, but I can't think of any other plausible answer.
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| 4 | weykool
ID: 2842717
Wed, Apr 15, 2009, 18:32
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5 would be correct.
You were right that one side of each disappears.
Two sides of the pyramid and the sides of the tetrahedron would form a 1x1 parellelagram.
The shape it would form would be the A frame on top of your square garage that ties into the A frame of your house if the two frames were at right angles.
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