UCLA Olga Radko Endowed Math Circle

1/23/2022 -- Advanced 1A: Josephus problem

Josephus and his forty soldiers were trapped in a cave. This means that there was a total of 41 fighters in the circle. Let us number 1 the first fighter to raise his sword, let us number 2 the fighter to his right, etc. The goal of this lesson is to solve the following two problems.

Problem 1 What was the position of Josephus in the circle?

Problem 2 Suppose that there are n soldiers, including Josephus, in the cave. What should the position of Josephus be in order for him to stay alive?