**Problem Statement **

King Arthur had knights over sitting in a round table. To determine who got the last dessert he made them play a game. King Arthur numbered the chairs from beginning with one and continuing around the table, with one knight in each chair he made them sit down to occupy the chairs. King Arthur then stood behind the knight in chair one, he said "You're in" Next, he moved to chair two and and said "You're out" and that knight would leave his seat. He continued around to chair three and said "You're in", Then said "You're out" to chair four. He continued to do this around the table. He would skip the chairs that he already got out. The winner of the table is the knight who doesn't get eliminated so their fate depends on which chair they are sitting in. We have to figure out a general rule or an equation

**Process**

Initially we started to try random small numbers like five and worked from there to see who would go out but, we then realized that we should try to start from one and go up from there to see if we can notice some sort of pattern so we organized our data in a table to see if could find a general pattern.

General Patterns we found:

- Every even number will be eliminated first round

- After a certain amount of people the pattern of the winner starts over

- Every root number of two the winner is one

General Patterns we found:

- Every even number will be eliminated first round

- After a certain amount of people the pattern of the winner starts over

- Every root number of two the winner is one

**Solution**

Eventually from these general rules we were able to come up with a formula. We realized that depending on the number of knights on the table you are supposed to find the closest root number of two. For example if there is a total number of 10 the closest root number of two would be 8 because 2^3 equals 8. After that step you are supposed to multiply the exponent closest to the number multiply it by two because the patter goes up by two and subtract by one because we know that every even number will get canceled. So, 3x2 is 6-1 equals 5. With 10 knights around the circle, the knight is chair five would win. The general formula that we came up with in order to figure out the winner for however many knights was...

**Evolution**

This group problem was a little bit different than the usual. Instead of my normal math table I had three new students who we had to work with which changed up the table dynamic a little bit more. With my normal table I usually find myself taking lead and pushing everyone to explain why they think what they think, or am the one who is answering question to help my group. This time, I was a little bit more in the position of asking questions, and I didn't feel quite as confident in this specific math problem. With the group I had it was really easy to just ask questions and have them explain their thought process which was really awesome, especially with the three new students. I found myself still being able to help my other peers with the things I did understand but, also follow along with my peers and ask whenever I needed the help. With a much bigger group I found that everyone had something to contribute, and it was really awesome seeing that whole process of understanding the problem, trying things out individually, gathering back as a group and discussing about it. Everyone was into the problem, we all did some things differently, which helped me understand the problem better and was definitely cool to see everyone so into the math problem. I would give myself an A+ because my group and I made sure we were on task and we were all so invested into the problem. We all contributed what we could, shared our ideas, and learned a lot from each toher alone.