bonanova Posted June 5, 2008 Report Share Posted June 5, 2008 Consider two solids: a unit-length tetrahedron [triangular base pyramid] and a unit-length square pyramid.The visible sides of these solids, if the single square face is placed on the table, are equilateral unit-length triangles. Glue a face of the tetrahedron to a face of the pyramid so that the points of the two triangles exactly coincide. How many faces does the new solid have? Quote Link to comment Share on other sites More sharing options...
0 Guest Posted June 5, 2008 Report Share Posted June 5, 2008 7? 5 (square pyramid) + 4 (tetrahedron) - 2 (faces that stick together) = 7 Quote Link to comment Share on other sites More sharing options...
0 bonanova Posted June 5, 2008 Author Report Share Posted June 5, 2008 7? 5 (square pyramid) + 4 (tetrahedron) - 2 (faces that stick together) = 7 Amazingly, that's not the answer. Why?This is a somewhat infamous puzzle question. It was given on a national [u.S.] test and the Educational Testing Service listed your answer as correct. It was challenged by a bright student and ETS was found to be in error. Later tests were screened by an expert panel before being administered. Quote Link to comment Share on other sites More sharing options...
0 Guest Posted June 5, 2008 Report Share Posted June 5, 2008 Amazingly, that's not the answer. Why?This is a somewhat infamous puzzle question. It was given on a national [u.S.] test and the Educational Testing Service listed your answer as correct. It was challenged by a bright student and ETS was found to be in error. Later tests were screened by an expert panel before being administered. 5 ! I haven't calculated yet, but base on your reply, I feel that the other 2 plane of the tetrahedron are so happen to be co-plane with 2 sides of the square pyramid. Tha't makes 2 surface become 1. Did I get your message right? Quote Link to comment Share on other sites More sharing options...
0 bonanova Posted June 5, 2008 Author Report Share Posted June 5, 2008 5 ! I haven't calculated yet, but base on your reply, I feel that the other 2 plane of the tetrahedron are so happen to be co-plane with 2 sides of the square pyramid. Tha't makes 2 surface become 1. Did I get your message right? Yup! Nice going. Doubters can construct the solids fairly easily to verify, but there's a quicker way to see it:Draw two square pyramids with touching sides of their square bases. Draw a line connecting their apexes. Observe that its length is unity, the same as all the other edges. Now note that the added line defines a unit-length tetrahedron between the pyramids. A moment's reflection shows that two of the tetrahedron's sides are coplanar with two of the pyramid's sides. Q.E.D. Quote Link to comment Share on other sites More sharing options...
0 Guest Posted June 5, 2008 Report Share Posted June 5, 2008 Yup! Nice going. Doubters can construct the solids fairly easily to verify, but there's a quicker way to see it:Draw two square pyramids with touching sides of their square bases. Draw a line connecting their apexes. Observe that its length is unity, the same as all the other edges. Now note that the added line defines a unit-length tetrahedron between the pyramids. A moment's reflection shows that two of the tetrahedron's sides are coplanar with two of the pyramid's sides. Q.E.D. Wow, thanks for your explanation. It makes my imagination clearer. And I would say your explanation are so simple and straight forward. Thank you This is a nice one! Quote Link to comment Share on other sites More sharing options...
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bonanova
Consider two solids:
- a unit-length tetrahedron [triangular base pyramid] and
- a unit-length square pyramid.
The visible sides of these solids, if the single square face is placed on the table, are equilateral unit-length triangles.Glue a face of the tetrahedron to a face of the pyramid so that the points of the two triangles exactly coincide.
How many faces does the new solid have?
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