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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.
The included problems are not arranged according to any specific order. [5] The book includes ideas that aimed to keep readers from boredom by adopting a wide variety of problems such as calculations of areas of rice fields, problems related to the construction of rivers and riverbanks, geometric progression, and the Josephus problem. The ...
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.
By the 20th century, Jewish attitudes toward Josephus had softened, as Jews found parts of The Jewish War inspiring and favorable to the Jews. The last stand at Masada was seen as inspirational rather than tragic, for example. A 1938 / 1941 play, Jerusalem and Rome, was loosely based on The Jewish War, and various novels were written. [10]
Josephus was eventually freed and given a place of honor in the Flavian dynasty, taking the name Flavius, and worked as a court historian with the backing of the Imperial family. In his work The Jewish War , the chief source on the Great Revolt, he provides detailed accounts of the sieges of Gamla and Yodfat , and of internal Jewish politics ...
Although Josephus says that he describes the events contained in Antiquities "in the order of time that belongs to them," [63] Feldman argues that Josephus "aimed to organize [his] material systematically rather than chronologically" and had a scope that "ranged far beyond mere political history to political institutions, religious and private ...