The five Earls of the West are scheduled to arrive at the King's Palace on each of the first five days of July. They have been called upon to settle some uprisings in the Kingdom. The first Earl will arrive on the first of July, the second will arrive on the 2nd of July and so on. Each Earl, 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 Earl's arrival. If he supports the king, all subsequent Earl's cancel their visits. An Earl's first priority is to remain alive, and his second priority is to become king. i. Draw a tree diagram to represent this information. ii. How many subgames are there? iii. Who is the King on the 6th day of July?