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An Apple a Day

A man entered an orchard through 7 gates, and there took a certain number of apples.  When he left the orchard, he gave the first guard half the apples he had and 1 apple more.  To the second guard he gave half his remaining apples and 1 apple more.  He did the same to each of the remaining five guards and left the orchard with 1 apple.  How many apples did he gather in the orchard?

Liber Abaci, Leonardo of Pisa, 1202

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"An Apple a Day," Convergence (April 2004)