I saw this puzzle in a local newspaper:
Consider a normal bicycle set to stand in its upright position, and its pedal is set to the position as shown in this figure. One man slightly hold the seat to keep the bicycle from falling. (Actually this is not important, there can be many ways to keep the bicycle from falling without affecting the experiment result). A non-elastic string is tied to the end of the pedal crank arm as in here. Another man then pulls the string backward.
The question is: In which direction will the bicycle move? Forward, backward, or standstill? Discuss possible cases.
Hint: The answer is non trivial. The readers are encouraged to try this experiment before coming to a hasty conclusion, since it's quite simple to carry out.
Despite the "Hint" part, and the "counter-intuitive" in the title, which is a quite clear suggestion that the bicycle will move in a counter-intuitive direction (backward instead of forward), many people still submitted answer such as "Forward, why not!!", or "Standstill" or "Forward, then as the crank move to 9 o'clock position, it will move backward". Of course they are not the correct answer.
Some people answered that it will move backward, but couldn't give a decent explanation.
My best guess is that this must have something to do with the size (radius) of the wheel, the radius of the crank arm, and the ratio of the crank gear and the wheel gear as well. If the bicycle moves forward, the crank bolt/shoulder will move as well, then the displacement of the crank does not simply equal to the displacement cause by the wheel rotating...
So what can be a simple, short explanation? And what can be a detail explanation with math and equations involved?