A Sample Masters Exam Question
A math class with n students sits in a circle to play mathematical chairs. The students choose an elimination number d and then count off in order, 1, 2, 3, . 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, . 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?

Hint: 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.