The three wisest sages in the land were brought before the king to see which of them were worthy to become the king's advisor. After passing many tests of cunning and invention, they were pitted against each other in a final battle of the wits. Led blind-folded into a small room, the sages were seated around a small wooden table as the king described the test for them. "Upon each of your heads I have placed a hat. Now you are either wearing a blue hat or a white hat. All I will tell you is this- at least one of you is wearing a blue hat. There may be only one blue hat and two white hats, there may be two blue hats and one white hat, or there may be three blue hats. But you may be certain that there are not three white hats." "I will shortly remove your blind folds, and the test will begin. The first to correctly announce the colour of his hat shall be my advisor. Be warned however, he who guesses wrongly shall be beheaded. If not one of you answers within the hour, you will be sent home and I will seek elsewhere for wisdom." With that, the king uncovered the sages' eyes and sat in the corner and waited. One sage looked around and saw that his competitors each were wearing blue hats. From the look in their eyes he could see their thoughts were the same as his, "What is the colour of my hat?" For what seemed like hours no one spoke. Finally he stood up and said, "The colour of the hat I am wearing is . . ."
This is a math riddle. What row of numbers comes next in this series? 1 11 21 1211 111221 312211 13112221 You must also tell why this number comes next.
