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Beyond the Call of Duty

Now given a that a guest on horseback rides 300 li in a day.  The guest leaves his clothes behind.  The host discovers them after 1/3 day, and he starts out with the clothes.  As soon as he catches up with the guest, the host gives back the clothes and returns home in 3/4 day.  Assume the host rides without a stop.  Tell how far can he go in a day?

Jiuzhang Suanshu (The Nine Chapters on the Mathematical Art), c. 100 BCE

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"Beyond the Call of Duty," Convergence (September 2008)