Reading the [autobiography of Richard Feynman][1], I struck upon the following paragraphs, in which Feynman recall when, as a student of the Princeton physics department, he used to challenge the students of the math department. 

> I challenged them: "I bet there isn't a single theorem that you can tell me ­­what the assumptions are and what the theorem is in terms I can understand ­­where I can't tell you right away whether it's true or false."  
It often went like this: They would explain to me, "You've got an orange, OK? Now you cut the orange into a finite number of pieces, put it back together, and it's as big as the sun. True or false?"  
"No holes?"  
"No holes."  
"Impossible! There ain't no such a thing."  
"Ha! We got him! Everybody gather around! It's So­-and­-so's theorem of immeasurable measure!"  
Just when they think they've got me, I remind them, "But you said an orange! You can't cut the orange peel any thinner than the atoms."  
"But we have the condition of continuity: We can keep on cutting!"  
"No, you said an orange, so I assumed that you meant a real orange."  
So I always won. If I guessed it right, great. If I guessed it wrong, there was always something I could find in their simplification that they left out.

Forgetting that most of this was probably done as a joke, with what theorem would you have answered to Feynman's challenge?


  [1]: https://en.wikipedia.org/wiki/Surely_You%27re_Joking,_Mr._Feynman!