The Linear Josephus Problem in Two Directions

The first process of elimination starts counting up from the first player and eliminates the player, the , and so on. The second process counts down from the player and eliminates the player, the , and so on. The first process comes first and the second process second at every stage. The direction changes at either end of the line.

For research on the variants of the Josephus problem, please see the following two papers written by the authors:

R. Miyadera, S. Hashiba, and D. Minematsu, "How High School Students Can Discover Original Ideas of Mathematics Using Mathematica," Mathematica in Education and Research, 11(3), 2006.

H. Matsui, T. Yamauchi, S. Tatsumi, T. Inoue, M. Naito, and R. Miyadera, "Interesting Variants of the Josephus Problem," Kokyuroku (to be published).