The Lucas Ship Problem

Every day at noon a ship leaves Le Havre for New York and another ship leaves New York for Le Havre. Each trip lasts seven days and seven nights. How many ships going east will a ship leaving Le Havre today meet during its journey to New York? Can you answer graphically?

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This problem was invented by Edoard Lucas, a French nineteenth-century mathematician.
Reference
[1] B. A. Kordemsky, The Moscow Puzzles, London: Penguin, 1990 p. 108, 273.
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