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The problem is named after Flavius Josephus, a Jewish historian and leader who lived in the 1st century. According to Josephus's firsthand account of the siege of Yodfat, he and his 40 soldiers were trapped in a cave by Roman soldiers. They chose suicide over capture, and settled on a serial method of committing suicide by drawing lots.
Josephus problem table: Image title: Claude Gaspar Bachet de Méziriac's interpretation of the Josephus problem with 41 soldiers and a step size of 3, visualised by CMG Lee. Time progresses inwards along the spiral, green dots denoting live soldiers, grey dead soldiers, and crosses killings.
The problem for graphs is NP-complete if the edge lengths are assumed integers. The problem for points on the plane is NP-complete with the discretized Euclidean metric and rectilinear metric. The problem is known to be NP-hard with the (non-discretized) Euclidean metric. [3]: ND22, ND23
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Josephus problem 30 9: Image title: Variant of the Josephus problem with 15 Christians and 15 Turks and a step size of 9, visualised by CMG Lee. Time progresses inwards along the spiral, green dots denoting live soldiers, grey dead soldiers, and crosses killings. Width: 100%: Height: 100%
Then it gives a proof that uses a different specific example ("we explicitly solve the problem when every second person will be killed"). But in no case does it actually give the answer. I believe the answer for the Josephus example of 41 participants and a step of three is that position 31 is the survivor and position 16 is the next-to-last.
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Rectangles: Problems regarding the area of a rectangular plot of land appear in the RMP and the MMP. [8] A similar problem appears in the Lahun Mathematical Papyri in London. [13] [14] Circles: Problem 48 of the RMP compares the area of a circle (approximated by an octagon) and its circumscribing square. This problem's result is used in problem ...