public class Test {
    /**
     * 初始化编号和密码表
     * **/
    private static final Map<Integer, Integer> map = new TreeMap<Integer, Integer>();

    static {
    map.put(1, 3);
    map.put(2, 1);
    map.put(3, 7);
    map.put(4, 2);
    map.put(5, 4);
    map.put(6, 8);
    map.put(7, 4);
    }

    /**
     * 初始化报数列表
     * **/
    public static void init(List<Integer> list, int n) {
    for (int i = 1; i <= 7; i++) {
        list.add(i);
    }
    }

    /**
     * 报数函数，所有人出列，就结束
     * **/
    public static void report(List<Integer> list, Map<Integer, Integer> map,
        int cipher, int x) {
    int size = list.size();
    if (size > 0) {
        Integer outIndex = 0;
        if (x + cipher < size) {
        outIndex = x + cipher - 1;
        } else {
        cipher = cipher - (size - x);
        outIndex = (cipher % size == 0 ? size : cipher % size) - 1;
        }
        Integer out = list.get(outIndex);
        cipher = map.get(out);
        System.out.println("outIndex:" + outIndex + "  out:" + out
            + "  cipher:" + cipher);
        list.remove(out);
        x = outIndex;
        report(list, map, cipher, outIndex);
    }
    }

    public static void main(String[] args) {
    List<Integer> list = new ArrayList<Integer>();
    init(list, 7);
    report(list, Test.map, 20, 0);
    }
}

------解决方案--------------------
运行结果如下：
outIndex:5 out:6 cipher:8
outIndex:0 out:1 cipher:3
outIndex:2 out:4 cipher:2
outIndex:3 out:7 cipher:4
outIndex:0 out:2 cipher:1
outIndex:0 out:3 cipher:7
outIndex:0 out:5 cipher:4
out代表出队人的号码，cipher是他执有的密码.

------解决方案--------------------
Java code

public class TestJosephus {

    /**
     * @param args
     */
    public static void main(String[] args) {
        Person person1 = new Person(1, 3, null);
        Person person7 = new Person(7, 4, person1);
        Person person6 = new Person(6, 8, person7);
        Person person5 = new Person(5, 4, person6);
        Person person4 = new Person(4, 2, person5);
        Person person3 = new Person(3, 7, person4);
        Person person2 = new Person(2, 1, person3);
        person1.setNextPerson(person2);
        new TestJosephus().josephus(person1, 20);

    }

    
    public void josephus(Person person, int m) {
        Person pPerson = person;
        //只有一个对象则不用遍历，直接输出来
        if (person.getNextPerson() == person) {
            System.out.print(" " + person.getNum());
        } else {
            //遍历得到person的前一个对象
            while (person != pPerson.getNextPerson())
                pPerson = pPerson.getNextPerson();
            //当前对象即要遍历对象之一，所以遍历数减一
            for(int i=1;i<m;i++){
                pPerson = person;
                person = person.getNextPerson();
            }
                
            System.out.print(" " + person.getNum());
            pPerson.setNextPerson(person.getNextPerson());
            person.setNextPerson(null);
            josephus(pPerson.getNextPerson(), person.getPassword());

        }
    }
}




public class Person {
    private Person nextPerson;
    private int num;
    private int password;
    public Person(int num, int password, Person nextPerson) {
        super();
        this.num = num;
        this.password = password;
        this.nextPerson = nextPerson;
    }
    public Person getNextPerson() {
        return nextPerson;
    }
    public int getNum() {
        return num;
    }
    public int getPassword() {
        return password;
    }
    public void setNextPerson(Person nextPerson) {
        this.nextPerson = nextPerson;
    }
    public void setNum(int num) {
        this.num = num;
    }
    public void setPassword(int password) {
        this.password = password;
    }
    
}