Problem Statement

King Arthur was a ruler in Camelot who had knights and a round table. If the King had something to give to his knights, he'd have to determine who'd get it. In order to determine who got it, he setup chairs in a circle around the table beginning with 1 and continued around the table with one chair for each knight. The knights sat down so that each chair was occupied and left King Arthur standing. When each knight was sitting, King Arthur stood behind stood behind the knight in chair 1 and said "You're In". He then moved on to the knight in chair 2 and said, "You're Out," and that knight left their seat and went to stand at the side of the room. Next, he moved on to the knight in chair 3 and said, "You're In". Then, he said "You're Out," to the knight in chair 4 and that knight left his chair. King Arthur kept going around the table in this manner. When he came back around to the knight in chair 1, he either said, "You're In" or "You're Out," depending on what he said to the previous knight. If a chair was empty, he automatically skipped it. He continued this process until only one knight was left sitting at the table. That knight was the winner. Now the question of the problem was: If you knew how many knights were going to be at the table, how could you quickly determine which chair to sit in so that you would win? Our task was to develop a general rule or formula that will predict the winning seat in terms of the number of knights.

Process

 My initial attempt was to create a x and y table. X being the number of knights and Y being the winner. I first started off with a random number of knights and worked my way until I had found the winner. My group mates tried other numbers and we shared with one another what we got so that we could start creating a table. When looking at the table, my group and I discovered that there was a pattern. We noticed that chair number one was always the winner when it was 2 to the power of something. We didn't know how to put this information into an equation, so that's when Mr. B showed us what the final equation looked like.

Solution

In this equation, X represents the number of knights there are. In the parentheses, what's happening is that we're finding out how far down X is from the last time the pattern rests. We then multiply 2 and add 1 which makes it odd and count off by 2.

evaluation/Reflection

What pushed my thinking was coming up with an equation that could easily find you the winning seat depending on how many knights there were. I would say that I was both challenged mathematically as well as my group interactions. I know that math is not my strongest subject and that affects me in a way where I am afraid to ask for help. I know when I am stuck and when I need help, but for some reason, I am unable to bring myself to ask for help. I don't feel confident in asking my peers for help when it comes to math specifically because I feel like I am going to ask a dumb question. I do feel that I am able to help those that are around me. I know that helping others try to understand will also help me reassure myself that I understand. I think my group did a pretty good job interacting during the first stages of a problem. I know that since we all created tables, we checked in with one another to make sure that we got the same answers. The grade I would give myself for this problem would be an A because although I did refrain from asking questions, I would listen to my group members explain their thought process and I would work through the problem based off what I knew.