Reading the autobiography of Richard Feynman, 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?

Reading the autobiography of Richard Feynman, 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?