Brilliant King Arthur's knights

package com.anlak.optimization;

import java.util.Iterator;
import java.util.LinkedList;
import java.util.List;


/*
 * There are p knights sitting at positions [1,2,...p] at King Arthur's round
 * table. In order to choose the leader, Arthur starts counting at position 1
 * and dismisses every rth seated knight until only 1 knight remains. The
 * remaining seated knight becomes the leader. Let C(p,r) be the integer
 * position of the eventual leader when the table starts out with p knights and
 * every rth seated one is dismissed. Let T =
 * C(999,11)+C(121,12)+C(2,1)+C(15,16)+C(99,3). What is T? Details and
 * assumptions C(4,2)=1. The knights start seated at positions 1, 2, 3, 4.
 * Arthur dismisses them in this order: 2, 4, 3. The knight seated at position 1
 * becomes the leader.
 */

public class Brillant
{
    public static int c( int n, int r )
    {
        List<Integer> x = new LinkedList<Integer>();

        for (int i = 1; i <= n; i++)
            x.add(i);

        Iterator<Integer> iter = x.listIterator(n);

        while (x.size() > 1)
        {
            for (int i = 0; i < r; i++)
            {
                if (!iter.hasNext())
                    iter = x.iterator();
                iter.next();
            }

            iter.remove();
        }

        return x.get(0);
    }

    public static void main( String[] args )
    {
        System.out.println(c(999, 11) + c(121, 12) + c(2, 1) + c(15, 16) + c(99, 3));
    }
}