Josephus problem - the most violent math problem | 3 different approaches

Описание: 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.

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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, part 7 of Josephus' The Jewish War

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Watch the video and Learn Something Extraordinary...
00:00​​ | What is Josephus problem (or Josephus permutation) ?
01:16 | Different approaches to solve this problem
01:29​​ | First Approach: The Recurrence Formula
04:58 | Second Approach: General Formula
06:28 | Third Approach: Binary Numbers (Simplest Method)
06:49 | Try yourself

This video will present an analytical solution to the problem

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