The circle of doom the puzzle's own namesake talked his way out of
Soldiers stand in a circle. Starting from one person, every second (or kth) person is eliminated as the count goes around, again and again, until only one remains. Where should you stand to be the survivor? Legend holds that the historian Flavius Josephus used exactly this reasoning to avoid a suicide pact with trapped Jewish rebels in 67 CE, maneuvering himself and a companion into the surviving positions.
Reveal the answer
For n people counting off by 2s, the survivor's position can be found from the binary representation of n: write n in binary, move the leading 1 to the end, and the resulting number is the safe position. For 41 people, for instance, the answer is position 19. Josephus is said to have used the equivalent trick to end up as one of the last two standing, then talked his companion into surrendering rather than dying — historians debate how embellished the story is, but the mathematical puzzle bearing his name is entirely real.
— Flavius Josephus, Josephus problem — The Jewish War, Book 3; puzzle named in his honor