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This problem was e-mailed to me by my friend Eric Wogsberg, who later informed me that it comes from a calculus book by Lipman Bers:

You are an architect.  Your client, living in Flatland, wants a building designed with a long 3 foot wide corridor which opens into a larger hallway.  You must design the hallway for the minimum width w that will allow the inhabitants to move a 24 foot-long pole down the corridor and turn it into the hallway. The corridor is perpendicular to the hallway.  Since this is Flatland, the pole cannot be tilted up.  The pole is rigid. How wide must the hallway be?