The following is a conceptually simple puzzle. Most 5 year olds will understand the objective (but fail to solve it) and most Ph.D's will do just as poorly as the 5 year old (unless they already know the solution, which anyone reading this post now knows).
Hand a person a tetrahedron that has been cut in two equal pieces (the provided link has a printable foldable 2D net). Tell them to put the two pieces back together to form a tetrahedron. Then watch them struggle to put it together again, fail and give up (or worse yet, conclude it is impossible).
I have this puzzle laying around on my desk and almost everyone has failed, including some very smart people. I gave it to someone with graduate studies in crystallography and they got it pretty quickly. As for the rest... fail. It is surprising to me that most people fail. There must be an optical illusion going on or something similar. Anyways, enjoy teasing your friends (or enemies).
Question: Know any similar geometric puzzles that are easy to explain and hard to solve?
From a paper rectangle create this shape. You may cut 3 straight line segments (no gluing) but there's a twist!
Note: This is not original - surely it must be ancient.