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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.
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
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.
Goldbach’s Conjecture. One of the greatest unsolved mysteries in math is also very easy to write. Goldbach’s Conjecture is, “Every even number (greater than two) is the sum of two primes ...
The principal source for the story of Theudas' revolt is Josephus, who wrote: . It came to pass, while Cuspius Fadus was procurator of Judea, that a certain charlatan, whose name was Theudas, persuaded a great part of the people to take their effects with them, and follow him to the Jordan river; for he told them he was a prophet, and that he would, by his own command, divide the river, and ...
If A answers da, C is Random, and B is the opposite of A. One can elegantly obtain truthful answers in the course of solving the original problem as clarified by Boolos ("if the coin comes down heads, he speaks truly; if tails, falsely") without relying on any purportedly unstated assumptions, by making a further change to the question:
Winnipeg Jets center Mark Scheifele (55) congratulates goaltender Connor Hellebuyck (37) after they defeated the Boston Bruins in an NHL hockey game, Thursday, Jan. 30, 2025, in Boston.
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.