The writings of Josephus Flavius, the first century Romano-Jewish historian and hagiographer whose accounts have shed light on the events of the First Jewish–Roman War, are inspiring serious debate two millennia later… among students and teachers of mathematics.
According to Josephus — born Yosef Ben Mattatiyahu and at one time a commander of Jewish troops in the Galilee — he and 40 other soldiers were trapped in a cave during the Roman siege of Yodfat, in the Galilee, in 67 CE. Rather than surrender, the troops chose to commit assisted suicide, through a process in which the soldiers killed each other rather than themselves. In his account, Josephus states that he and another man remained until the end of the process, when they decided not to kill themselves and to surrender to the Romans instead.
The tale has given rise to a mathematical problem titled the “Josephus permutation,” asking, in essence, what it would take to remain the last man standing in a suicide circle.
A recent video on the popular Numberphile YouTube channel examines the theory.
In the video, Daniel Erman from the University of Wisconsin-Madison describes the problem as follows: The soldiers are standing in a circle, waiting to be executed by one of their comrades. Counting begins at one point in the circle and proceeds around the circle in a specified direction. The first soldier executes the man nearest to him. The soldier standing in the spot next to the man that was just executed proceeds to kill the man nearest to him. The procedure is repeated with the remaining soldiers until only one person remains.
Which person ends up alive after this process? Watch the video above to find out. You never know when it might come in handy.