Josephus problem

In computer science and mathematics, the Josephus Problem (or Josephus permutation) is a theoretical problem related to a certain counting-out game.

People are standing in a circle waiting to be executed. Counting begins at a specified point in the circle and proceeds around the circle in a specified direction. After a specified number of people are skipped, the next person is executed. The procedure is repeated with the remaining people, starting with the next person, going in the same direction and skipping the same number of people, until only one person remains, and is freed.

The problem — given the number of people, starting point, direction, and number to be skipped — is to choose the position in the initial circle to avoid execution.

History

The problem is named after Flavius Josephus, a Jewish historian living in the 1st century. According to Josephus' 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 states that by luck or possibly by the hand of God, he and another man remained until the end and surrendered to the Romans rather than killing themselves. This is the story given in Book 3, Chapter 8, par 7 of Josephus' The Jewish War (writing of himself in the third person):

Josephus

Titus Flavius Josephus (/dʒoʊˈsiːfəs/; 37 – c. 100), born Joseph ben Matityahu (Hebrew: יוסף בן מתתיהו, Yosef ben Matityahu), was a first-century Romano-Jewish scholar, historian and hagiographer, who was born in Jerusalem—then part of Roman Judea—to a father of priestly descent and a mother who claimed royal ancestry.

He initially fought against the Romans during the First Jewish–Roman War as head of Jewish forces in Galilee, until surrendering in 67 CE to Roman forces led by Vespasian after the six-week siege of Jotapata. Josephus claimed the Jewish Messianic prophecies that initiated the First Roman-Jewish War made reference to Vespasian becoming Emperor of Rome. In response Vespasian decided to keep Josephus as a slave and interpreter. After Vespasian became Emperor in 69 CE, he granted Josephus his freedom, at which time Josephus assumed the emperor's family name of Flavius.

Flavius Josephus fully defected to the Roman side and was granted Roman citizenship. He became an advisor and friend of Vespasian's son Titus, serving as his translator when Titus led the Siege of Jerusalem, which resulted—when the Jewish revolt did not surrender—in the city's destruction and the looting and destruction of Herod's Temple (Second Temple).

Josephus (disambiguation)

Josephus (37 – c. 100) was a Roman Jewish historian.

Josephus may refer to:

People:

Fictional characters:

Josephus (grandfather of Josephus)

Josephus (Greek: Ἰώσηπος; flourished 1st century BC and 1st century, born about 30 BC) was an ethnic Jew living in Jerusalem.

Josephus was the son born to Matthias Curtus and his unnamed Jewish wife. He came from a wealthy family and through his father he descended from the priestly order of the Jehoiarib, which was the first of the twenty four-orders of Priests in the Temple in Jerusalem. His paternal grandparents were Matthias Ephlias and the daughter of the High Priest Jonathon. Jonathon may have been Alexander Jannaeus, the High Priest and Hasmonean ruler who governed Judea from 103 BC-76 BC.

He was a contemporary to the King Herod the Great and the Herodian Dynasty governing Judea and the surrounding territories. Josephus followed his paternal ancestors and served as a Priest in the Temple in Jerusalem.

Josephus married an unnamed Jewish noblewoman. The wife of Josephus was a distant paternal relative of his, as she was a descendant of his paternal great-grandfather Simon Psellus. His wife bore him a son, Matthias. Through his son, he would be the paternal grandfather of the Roman Jewish Historian of the 1st century, Flavius Josephus.