Instructor's output for Josephus permutation cannot be reproduced

Question

I'm in a data structures class and am unable to reproduce the example data given by an instructor. The problem is the classic Josephus problem with a user supplied number of members, step interval, and starting position.

Specifically, I'm told that 99 people, starting on 23, counting off by 5 should leave 84 as the last man standing.

I come up with: 65. I ran again thinking the input may have been 99 people, starting at 5 with an interval of 23. This produced: 42.

My assignment solution involves a circular linked list, however this c code produces the same output in all cases:

#include <stdio.h>

int josephus(int n, long k)
{
  if (n == 1)
    return 1;
  else
  /* The position returned by josephus(n - 1, k) is adjusted because the
   *        recursive call josephus(n - 1, k) considers the original position 
   *               k%n + 1 as position 1 */
 return (josephus(n - 1, k) + k-1) % n + 1;
}

int main()
{
int n = 99;
int k = 23;
printf("The chosen place is %d\n", josephus(n, k) + 5);
return 0;
}

Thanks again.

Answer 1

LaFore sees counting off to be stepping over. I.e., starting at 1, counting by two will kill person 4 first. The text does have one example buried in it. This is not intuitive and LaFore seems to be the only author counting this way.