How to Survive a Josephus Game by David Aribiyi '19, Monday, December 3, 1 - 1:45 pm

How to Survive a Josephus Game by David Aribiyi ’19, Monday, December 3, 1 – 1:45 pm, Stetson Court Classroom 101, Mathematics Colloquium

Abstract:  In the Original Josephus Game, n players stand in a circle. Starting at the first player, the game proceeds with each player killing (read: removing) the player to the left of them until only one is left.  The problem is figuring out what position to stand in to ensure you survive the game. Historically, this has been a relatively easy problem to solve, with many solutions pointing out a simple pattern that emerges as you increase n.  However, what would happen if we vary the number or players removed at a time?  Or the number of players skipped at a time?  Or the number of times a player is removed before they are “really” removed?  In my colloquium, we will look at how Josephus games have grown and morphed over time and how the seemingly simple problem of finding the survivor has grown more complex.  I will also prove some explicit and recursive formulas for computing survivors of specific games.