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Shitikanth Kashyap
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No points if you don't get it right the first time.
Puzzle: Suppose a long tray of water with wheels is resting on a smooth flat surface.  At the left end of the tray, floating in the water, is a remote-controlled toy boat.  You turn it on and it moves toward the right end of the tray.  When it reaches the other end, you turn it off.  How much does the tray move from its initial position?

Suppose the length of  the tray is L, the mass of the tray and water is M, and the mass of the boat is m.  Ignore friction! 

Again, this is from Mark Levi's book of physics puzzles.

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