class with ÒnÓ students sits in a circle to play mathematical chairs. The students choose an elimination number ÒdÓ and then count off in order, 1, 2, 3, É . When the count gets to d, that student
is eliminated from the game. The next
student starts the count over and the
students count 1, 2, 3, É . Again, when the count
gets to d, that student is eliminated. Continue in this manner until only one student is left. That student wins the game.
¥Where should you sit in order to win the game?
Solve the problem first for elimination number 2 or 3 and then try to solve it for elimination number d.
¥Note: This is a version
of The Ring of Josephus problem.