5. (20 points). The ten Dukes of Earl are scheduled to arrive at the royal palace on each of the rst ten days of May. Duke One is scheduled to arrive on the rst day of May, Duke Two on the second, etc. Each Duke, upon arrival, can either kill the king or support the king. If he kills the king, he takes the king's place, becomes the new king, and awaits the next Duke's arrival. If he supports the king, all subsequent Dukes cancel their visits. A Duke's rst priority is to remain alive, and his second priority is to become king. Who is king on May 10