Futility Closet

“The Pup Tent Problem”: Solution

Posted in Puzzles by Greg Ross on June 13th, 2009

Solution to The Pup Tent Problem:

The test makers were expecting the answer (C), but several students pointed out that in fact (A) is correct — the shapes fit together to produce a surprisingly simple object with only five faces.

This is easiest to see if you imagine two square pyramids side by side: The tetrahedron fits precisely between them to make a smooth-sided “pup tent”:

http://commons.wikimedia.org/wiki/File:Pyramid_(PSF).png

If you have polyhedral dice, try fitting the face of a 4-sided to an 8-sided die; you’ll find that the adjoining sides are coplanar.