A Sample Masters Exam
math 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.
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.