The Josephus Problem

The Josephus Problem is a problem in computer science based on a counting-out game. The problem is named after Flavius Josephus, a Jewish-Roman historian from the 1st century, who tells the story like this:

“A company of 40 soldiers, along with Josephus himself, were trapped in a cave by Roman soldiers during the Siege of Yodfat in 67 A.D. The Jewish soldiers chose to die rather than surrender, so they devised a system to kill off each other until only one person remained. (That last person would be the only one required to die by their own hand.)

All 41 people stood in a circle. The first soldier killed the man to his left, the next surviving soldier killed the man to his left, and so on. Josephus was among the last two men standing, “whether we must say it happened so by chance, or whether by the providence of God,” and he convinced the other survivor to surrender rather than die.”

This story gives rise to an interesting maths problem: If you’re in a similar situation to Josephus, how do you know where to stand so you will be the last man standing?

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