A regular tetrahedron has four equilateral triangles as faces. A regular square pyramid has four equilateral triangles and a square as faces. The faces of the tetrahedron are congruent to the triangular faces of the square pyramid.
A new polyhedron is created by gluing the tetrahedron and the square pyramid together at a triangular face so that the vertices of the triangles coincide. How many faces does this polyhedron have?
(In reply to re: Surely not the intended solution ! (spoilers)
I also fell for the "duh, it's 7" answer when this problem was in the
queue. I'm glad that Charlie showed me the error of my thinking
(as I was not impressed by, what I thought was, the trivial nature of this problem).
It would have been a shame to have missed having this problem on the site!