Problem Statement
The task is to find a formula or pattern to find out which chair a knight should sit in to become the winner. The way the game works is that King Arthur chooses who the winning knight is by having them sit at a round table and he goes around telling the first knight he is in and the next knight he is out and so on. The knights that lose or get told "You're out" leave the table, and the rest stay in, unless the King says "You're out" on the next round he goes around. King Arthur continues going around the table, until only one knight is left at the round table, the last knight at the table is the winner.
Process
At first we began doing what every group was doing which was to draw out what was happening and try to find a pattern based off that. You can what this looked like to the left. After a while we decided to create a table so we could display our results and possibly find a pattern from looking at the table, which we did. The pattern we found was at every base-2 number the winning seat would be, seat #1. This pattern was the most important because at the end it is what the formula is based off of. The other patterns/rules we found were to never sit in a even number chair, if the number of knights is even never sit in chair #3 and #7 and if the number of knights is odd never sit in chair #5 and #9. |
Solution
I would't call it solution because we found a lot of rules and other factors before finding the formula. The rules we found first were that you should never sit in a chair that is an even number, the second rule was that if the number of knights was an even number then you should avoid sitting in chair #3 and #7 and finally if the number of knights was odd you should avoid sitting in chair #5 and #9. Those rules helped out but what we really wanted to know was what seat to sit on to win every time no matter how many knights were there. So with the help of the patterns we saw and google we came up with this (X-R) x 2+1 x= # of knights - R= nearest lowest reset point.
Evaluation
In the beginning this problem was everything but easy and I admit I began to get a bit frustrated but I knew that I had to keep trying to find a solution. As I kept making more and more diagrams I noticed Mr. C going around mentioning something to groups that we hadn't figured out yet, I decided to ask him what it was because the last thing I wanted was for my group to fall behind in this problem. This is something I tend to do in every class but in math is where I find it to be most important especially since we are working with formulas and steps and if you miss something in the process of the problem it can affect you in a really bad way since you won't be able to use the formula or solve problem. Asking questions when Im confused is something I have never back down from because I know teachers will always support you and help you out the most they can and it's also for your own good. I felt like my group worked well but not great because the first day it felt like we didn't make much process other than find the patterns and rules which was a key component but we wanted the formula which made us get frustrated. For the group test I felt like we had some experience on approaching the problem and we were able to find the same rules pretty much just inverted but we couldn't find the formula. If I had to grade myself I would give myself an A- because I feel like I put in a lot of effort into trying to figure out this problem but I could've been a better group member and I feel like I didn't complete the task of finding a formula for the quiz.