Problem Statement
In this problem we had to figure out what seat we had to sit in to win the game. The game was King Arthur would go around the table and tell each night if they were in or they were out. He would do it by telling every other one that he was out and as they got out they would step to the side. We had to figure out which seat we have to sit in to win the game.
Process
My first attempts on this problem were to make a x and y table of the possibilities so that I can get an idea of how the seats were moving around. I did figured those out by drawing the knights in a straight line and basically going in and out and crossing out the ones that were out each round and kept going until I found a winner. After doing that for enough knights we saw a pattern beginning to form. We knew that it was always going to be an odd number and from there we saw that it would reset at a number that had something to do with 2 to the power of something. We noticed that it would reset at each of the powers of 2 and that is how we began to solve the problem.
Solution
To solve this problem you don't necessarily need an equation but if you have one you can solve for the winner much faster than you would if it was the original way I did it. Ok so the formula that my group came up with was S=( K-2^P)2+1. What all of this stands for is that the s is the winning seat, the K stands for the number of knights and 2^p is two to the highest power before the number of knights that you are using so for example if it was 7 it would be 2^2 because that is the highest power within the number. We then multiply it by two and add one because it has to be a negative number and we are subtracting the highest power of two. And to make sure it is an odd number we added the one. So if you and playing and you are trying to find the winning seat just know what the all of the powers of 2 and memorize the equation.
Reflection/Evaluation
In this problem the thing that pushed my thinking the most is that we had to come up with an equation/ rule for any number of knights. I think that I was more challenged by the group work than I was by the math content because I am more of an independent person what it comes to math and how I solve problems differently than others that solve them. I know when I am struggling because I usually get stuck and once I am given a hint I know that I can get it from there. I will usually be able to go from there and get a little further or even talk to the people around me and ask what they are doing. I do feel confident to ask for help because I know that at this school the teachers are always willing to help and I know that if I feel safe in an environment I will ask for help because of the people that I work with make me feel in a way safe. I think that I can help others around me because I know I actually learned the subject or the unit if I am able to let my group know what is going on. During the initial steps of the problem my group relied on what Ivanna and I came up with and we just built on top of the base ideas that Ivanna and I had. I think that the group quiz made me think but I don't think it made me work better with my group because I was trying to work through it as my group mates were working through it and we would just check in with each other. I think I deserve an A because I actually tried on this problem and that made my thinking go further than it would if we were doing the same problem on our own. I think the questions that I answered in my group showed how much I actually understood this problem and enjoyed it.