3. The Josephus problem is the following game: N people, numbered 1 to N, are sitting in a circle. Starting at person 1, a hot potato is passed. After M passes, the person holding the potato is eliminated, the circle closes ranks, and the game continues with the person who was sitting after the eliminated person picking up the hot potato. The last remaining person wins. Thus if M =0 and N=5, players are eliminated in order and player 5 wins. If M=1 and N=5, the order of elimination is 2,4,1,5.\