This is a puzzle of Martin Gardner, taken verbatim from My Best Mathematical and Logic Puzzles:
Two identical bolts are placed together so their grooves intermesh. If you move the bolts around each other as you would twiddle your thumbs, holding each bolt firmly by the head so it does not rotate and twiddling them in the direction shown below, will the heads
(a) move inward,
(b) move outward, or
(c) remain the same distance from each other?
I got the correct answer, though I couldn't really intuitively grasp why it was correct. The book offers the following answer and explanation (mouse over for spoilers):
The answer is (c): the situation is comparable to a person walking up an escalator at the same rate it is moving down.
The top google results for this puzzle pretty much quote this solution without further comment. Perhaps I'm just dense, Gardner's answer doesn't really feel like an explanation. Therefore, I've posted this problem for two reasons:
To give people who haven't seen this puzzle a chance to enjoy it, and
To get some satisfying explanations which make me say, "Oh, of course that's why that answer correct!".