The Josephus Problem is defined as follows :
Suppose n people are arranged in a circle and we are given a positive integer m <= n. Starting with a designated person, proceed around the circle removing every m th person. After removal, counting continues around the remaining circle. When all n people have been removed, the order in which the removal has occured defines the (n, m)-Josephus Permutation of the integers 1,2,...,n.
Use the + and - buttons to vary the value of m. The Josephus button displays the permutations for n=1 to n=100. The Survivor button displays the last person to be removed from the circle using an algorithm found here :
m :

The Josephus permutations for n=1 to n=100.