King Arthur Problem

King ARTHUR

Problem Statement:

This semester we were presented with an interesting problem it involved King Arthur and his nights. Our overall objective was to be able to identify who the winning knight in a game would be. The game consisted of all the knights sitting in a circle assigned with a number counting from one all the way to the last knight. Each round of the circle there would be a pulse of animation it would be inn and out, begging with 1 which would be inn.

Process:

Noting this we came to a conclusion that at the first round around the circle all of the even numbers were illuminated nothing that we still need to come to find how to easily identify who would be the winning knight.

What my group and I decided to do was to divide the work and start collecting data to potentially find a pattern. We decided to by hand collect the winners for several numbers and set an x and y chart the x being the total number of knights and the y being the winning number. After collecting various points we came to this.

We realized that alter the points match the pattern repeats.

We tried to observe now and look for patterns, we realized that

Then we realized that at that matching number there from 2^x there all exponents of 2 knowing this we could set up solid rules expressing that to understand what the winning number was dependent on the total number and where it lay in the pattern, we could do this my finding what 2^x was it closest to.

Solution:

After finding that pattern we began by formatting a formula we knew that we needed. Realizing that there were certain things we had to do in order to produce the correct answer. We were working on how to piece it together in mathematical terms. My group and I found out there would have to be a link to a logarithm yet we didn't know how to embedded it. We finally came to the conclusion that the formula was.

Evaluation/Reflection:

The group quiz was really fun actually. It definitely pushed our thinking because it was similar to the other problem yet you really had to understand the differences and what had changed. My group and I began by trying to understand what the problem was saying in this new game, then we split the different numbers we wanted to test and gathered data. This was great because communication was key in this process, if we were unsure of whether we had done a number correctly we would have the trust to ask a group mate to double check it. As we compiled our information we really pushed each other to understand the concept and discover a pattern and if one groupmate would discover something we would ask questions and share the new discovery. I liked this group quiz because in the initial problem I had an alright understanding yet this group quiz really pushed my group mates and I to deeply understand the concept and be able to repeat the problem solving process.