What is the last number, if we delete nth number of a circle ?

Question

If we delete the mth number from a circle which is composed of numbers 0, 1, …, n-1 counting from 0 at every time, what is the last number?

For example, a circle is composed of five numbers 0, 1, 2, 3, 4. If we delete the 3rd number at every time, the deleted numbers are in order of 2, 0, 4, 1, so the last remaining number is 3.

Answer 1

Its called Josephus problem http://en.wikipedia.org/wiki/Josephus_problem

int remaining(int n, int k) {
    int i, r = 0;
    for (i = 2; i <= n; i++)
        r = (r + k) % i;

    return r;
}

main()
{
    printf("%d\n", remaining(5, 3));
}