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	\problem{The Lucas Problem}

	This problem was invented by Edouard Lucas, a French nineteenth-century mathematician. \\
	``Every day at noon,'' Lucas said, ``a ship leaves Le Havre for New York and another ship leaves New York for Le Havre. The trip lasts 7 days and 7 nights. How many New York-Le Havre ships will the ship leaving Le Havre today meet during its journey to New York? Can you answer graphically?

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