PROBLEM Around King Arthur's Table OF THE WEEK King Arthur, the ruler of Camelot, loves inviting his knights over for parties around his round table. If there is something pleasant the king can give to only one knight-like an extra dessert or a dragon to chase-he has them play a game to determine who will get it. The game goes like this. First, King Arthur puts numbers on the chairs, beginning with 1 and continuing around the table, with one chair for each knight. He has the knights sit down so every chair is occupied. The king then stands behind the knight in chair 1 and says, "You're in." He moves to the knight in chair 2 and says, "You're out," and that knight leaves his seat and goes to stand at the side of the room to watch the rest of the game. The king next moves to the knight in chair 3 and says, "You're out." Then he moves to the knight in chair 4 and says. "You're in." The knights that are out leave the game.The king continues around the table in this manner. When he comes back around to the knight in chair 1, he says either "You're in" or "You're out," depending on what he said to the previous knight. He plays the game IN--OUT--OUT--IN--OUT--OUT--IN--OUT-- OUT-IN.. until only one knight is left sitting in King Arthur's Table. The king keeps moving around and around the table, alternately saying, "You're in" or "You're out" to the knights who remain at the table. If a chair is now empty, he simply skips it. He continues until only one knight is left sitting at the table. That knight is the winner. Use the following table to collect your data. Number of knights Winning chair number 1 to 101 or moreo Your Task The number of knights varies from day to day, depending on who is sick and who is out chasing dragons. Sometimes there are only a few, and sometimes there are over a hundred! Here's the big question of this POW. If you know how many knights are going to be at the table, how can you quickly determine which chair to sit in so that you will win? Your task is to develop a general rule, formula, or procedure that will predict the winning seat in terms of the number of knights present. The number of knights present depends on your birthday. For example, if you were born on June 20th, then you have 620 knights. If you were born on January 1st, then you have 101 knights. If you were born December 31, then you have the most knights. Every birthday must have two digits. Your goal is to develop a formula or procedure to determine the winning chair given a specific number of knights present. Be sure to explain why your rule works.