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A Math/Logic/Geometry Problem  
User currently offlinetimz From United States of America, joined exactly 15 years ago today! , 6835 posts, RR: 6
Posted (1 year 9 months 2 weeks 4 days 17 hours ago) and read 1681 times:

From one of those Litton ads in the 1960s:

All the faces on a certain polyhedron are triangular; the polyhedron has nine vertices. At six of the vertices, six triangles meet; at the other three vertices, four triangles meet. How many faces does the polyhedron have?

8 replies: All unread, jump to last
 
User currently offlineSmittyOne From , joined Dec 1969, posts, RR:
Reply 1, posted (1 year 9 months 2 weeks 4 days 4 hours ago) and read 1534 times:

Thanks Tim, my head just exploded like JFK in the Zapruder video.

User currently offlineyooyoo From Canada, joined Nov 2003, 6057 posts, RR: 50
Reply 2, posted (1 year 9 months 2 weeks 4 days 1 hour ago) and read 1483 times:

the answer is ...... ice cream.


I am so smart, i am so smart... S-M-R-T... i mean S-M-A-R-T
User currently offlineBirdwatching From Germany, joined Sep 2003, 3822 posts, RR: 51
Reply 3, posted (1 year 9 months 2 weeks 4 days ago) and read 1463 times:

The answer is 42

Soren   



All the things you probably hate about travelling are warm reminders that I'm home
User currently offlinevikkyvik From United States of America, joined Jul 2003, 10024 posts, RR: 26
Reply 4, posted (1 year 9 months 2 weeks 4 days ago) and read 1440 times:
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Quoting Birdwatching (Reply 3):
The answer is 42

Hey, and now we finally know the question too!

I shall go make myself a jynnan tonnyx in celebration.



"Two and a Half Men" was filmed in front of a live ostrich.
User currently offlinetimz From United States of America, joined exactly 15 years ago today! , 6835 posts, RR: 6
Reply 5, posted (1 year 9 months 2 weeks 3 days 21 hours ago) and read 1405 times:

Last night I decided the answer was 16 faces. Still can't decide whether a polyhedron meeting the given conditions can exist-- anybody know how to figure that?

User currently offlineNoWorries From United States of America, joined Oct 2006, 539 posts, RR: 1
Reply 6, posted (1 year 9 months 2 weeks 3 days 20 hours ago) and read 1378 times:

I can't visualize how that would work. Four triangles meeting at a vertex gives us a (four-sided) pyramid with a square base. In order to "hide" the square base, the only thing that I can think of is to join the pyramids at the opposite edges of their bases. That gives three vertices with four triangles and six vertices where five triangles meet (if I'm visualizing correctly) -- essentially three four-sided pyramids glued to the three rectangular faces of a triangular prism -- that's as close as I can get and that gives 14 sides.

User currently offlinetimz From United States of America, joined exactly 15 years ago today! , 6835 posts, RR: 6
Reply 7, posted (1 year 9 months 2 weeks 3 days 20 hours ago) and read 1367 times:

Maybe the polyhedron that I described doesn't exist-- I remembered the problem wrong. The correct version is: nine vertices, at six of which four triangles meet, and at the other three vertices six triangles meet. And the correct answer for that is 14 faces.

User currently offlinevikkyvik From United States of America, joined Jul 2003, 10024 posts, RR: 26
Reply 8, posted (1 year 9 months 2 weeks 3 days 20 hours ago) and read 1353 times:
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Quoting timz (Reply 7):
Maybe the polyhedron that I described doesn't exist-- I remembered the problem wrong. The correct version is: nine vertices, at six of which four triangles meet, and at the other three vertices six triangles meet. And the correct answer for that is 14 faces.

You have a picture of that? A septagonal bipyramid is almost that (it has 14 faces and 9 vertices), except that at 7 vertices, 4 triangles meet, and at 2 vertices, 7 triangles meet.

Or a Triaugmented triangular prism, which has 9 vertices and 14 faces, but at 3 vertices, 4 triangles meet, and at 6 vertices, 5 triangles meet.



"Two and a Half Men" was filmed in front of a live ostrich.
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