Josephus Flavius game

Josephus Flavius was a famous Jewish historian of the first century at the time of the Second Temple destruction. During the Jewish-Roman war he got trapped in a cave with a group of 40 soldiers surrounded by romans. The legend has it that preferring suicide to capture, the Jews decided to form a circle and, proceeding around it, to kill every third remaining person until no one was left. Josephus, not keen to die, quickly found the safe spot in the circle and thus stayed alive.

The applet below generalizes that situation. The number of people is limited by 50, but "Every which" controls allow for variations on the original theme. A player selects a spot and presses one of the Fast or Slow buttons to observe the sequence in which people will die. The purpose of the game, of course, is to stay alive by choosing the right spot. The counting starts from the topmost position indicated by a short straight line segment.

• Josephus Flavius problem
• Two ancient variants
• A simple solution
• Partial recursive solution
• A problem from USAMTS

Reference

R. Graham, D. Knuth, O. Patashnik, Concrete Mathematics, 2nd edition, Addison-Wesley, 1994.