When 17 year old found a mistake on the PSAT exam

A tetrahedron and a pyramid have edges of equal length. If they are glued together on a triangular face with the vertices aligned, how many faces will the new shape have?

This question is trickier than it looks! It stumped the test-makers.

Playable demonstration: Steve Phelps has made a Geogebra worksheet that you can try it out for yourself
http://tube.geogebra.org/student/m144...

Blog post: http://mindyourdecisions.com/blog/201...

References:
Pyramid Power: Searching for an Error in Test Scoring with 830,000 Helpers. Howard Wainera. The American Statistician. Volume 37, Issue 1, 1983.
http://onlinelibrary.wiley.com/doi/10...

New York Times. "Youth Outwits Merit Exam, Raising 240,000 Scores." Edward B. Fiske. March 17, 1981.
http://www.nytimes.com/1981/03/17/us/...

In researching this video, I found this problem was featured in the New York Times Worldplay puzzle a couple years ago: http://wordplay.blogs.nytimes.com/201...

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