I grew up on Martin Gardner in the 70's and 80's, so I'm always happy to see him referenced. My favorite physics puzzle of his is: If you heat a solid iron torus, does the radius of the hole in the middle grow or shrink?
You can gain a bit of intuition about growing and shrinking circles by imagining them to be squares with _very_ rounded corners, or equivalently, imagining what happens if you lengthen them by inserting straight lengths in four places, turning them into squares with very rounded corners.
For example, the old question of: if you have a rope lying on the surface of the earth all the way around a great circle, and make it 10m longer, how high could it be above the surface?
Even though the square-with-corners thing helps me visualize it quite perfectly, I _still_ find it weird that that the answer is 1.5m!