Urban Legends (Jacques Hadamard)
At the Bologna Congress, the meetings started in Bologna and ended in Florence. That's about a three-hour train ride and for this there was a special train. Hadamard was placed in a compartment of particularly noisy mathematicians, but he himself was tired and wanted to have some peace. Rather than simply try and ask the group to settle down (and since they were easily excitable mathematicians, this would likely be ineffective anyway), he instead posed aloud in the compartment a puzzle -- a rather difficult problem. Very quickly, everyone started working on the puzzle, and it suddenly became quiet so Hadamard could sleep.
-- Polya was one of the mathematicians in the compartment, and he tells this story in A Polya Picture Album, Boston: Birkhauser, 1987, p. 87.