King's Coins Problem On a cloudy day, a king went into the countryside with a bag of gold coins. The first person was one of his subjects who had recently lost one of his sons to the plague. The king gave this man half of the coins in his coin bag and then gave him two more coins. Then he continued walking down the road. Next the king met a merchant who had recently lost one of his ships to pirates. The king gave the merchant half of the coins in his coin bag and then he gave the merchant two more coins. By this point the king was getting tired. So, he turned around and headed back to his castle. On his way, he met his son the prince who was headed out into the countryside for some horseback riding. To the prince, the king gave half of the coins he had left in his coin bag and then two more. When the king got back to the castle he had two coins left. How many coins were in the king's coin bag when he left the castle on this cloudy day?