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Water Reeds

A pond has two water reeds, where the one grows 3 feet and the other 1 foot on the first day. The growth of the first becomes each day half of that of the preceding day, while the other grows twice as much as on the day before. In how many days will the two grow to equal heights?

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

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"Water Reeds," Convergence (December 2011)