King Arthur's Problem

King Arthur's daughter wanted to marry. She loved maths and created a problem for King Arthur's knights to solve. The knight who solved the problem would prove himself to be logical and brave, therefore worthy to become the lucky husband. The knights were told of the problem in advance and could choose whether or not to compete for the daughter's hand, but they were not told that King Arthur would not actually chop off anyone's head. All of the knights were to gather and be seated at the round table, then King Arthur would point to the knight in the first chair and tell him, "You live." To the next, rather unlucky knight, King Arthur would point and say, "You die." To the third knight he would say, "You live," and to the fourth, "Off with your head!" He would continue doing this around the table, chopping off the head of every other knight, until only one knight remained alive. The remaining knight would marry King Arthur's daughter. Where is the safe seat? Find the safe place to sit with different numbers of knights. Find a pattern so you can predict where to sit no matter how many people are seated in the circle. You need a strategy and method for recording your findings such as, when there are 12 knights, the safe seat is ___; when there are 20 knights, the safe seat is ___. Think about your strategy, then talk to a friend before you begin. You may work with a partner if you wish. Be sure to put both names at the beginning of your post when you share your discoveries.