A note in the margin reads:Our final introductory example is a variant of an ancient problem named for Flavius Josephus, a famous historian of the first century. Legend has it that Josephus wouldn't have lived to become famous without his mathematical talents. During the Jewish-Roman war, he was among a band of 41 Jewish rebels trapped in a cave by the Romans. Preferring suicide to capture, the rebels decided to form a circle and, proceeding around it, to kill every third remaining person until no one was left. But Josephus, along with an unindicted co-conspirator, wanted none of this suicide nonsense; so he quickly calculated where he and his friend should stand in the vicious circle.
In our variation, we start with
npeople numbered1tonaround a circle, and we eliminate every second remaining person until only one survives.
(Ahrens [5, vol. 2] and Herstein and Kaplansky [156] discuss the interesting history of this problem. Josephus himself [166] is a bit vague.)Last but not least, the other note in the margin says:
... thereby saving his tale for us to hear.
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