Gigi Gans 9/21 Dr.Drew Class A The Checkerboard problem Write up
The main question this problem is asking is how many possible boxes you can make in an 8x8 checkerboard square. Including the 64 single boxes and overlapping squares as well. They also showed a 3x3 square as an example for the different sizes you could use.
My first approach to this project was to start counting all of the 2x2 squares I could make. I started to tally all of them row by row and overlapping. I knew that there would somehow be a faster way or equation to speed up the problem but I couldn’t think of anything so I just started to count. The tallies weren’t really doing a lot for me and helping me get an idea of how many boxes I could make. It seemed like a waste of time and as If I wasn’t getting anything done. But I Still could not think of anything better than to just keep counting so I continued to count the 2x2 squares very carefully so I would not forget to count one or count the same one twice. This took about 30 -45 minutes of counting 2x2 squares until one of my table members Dominick explained his way of thinking. And I didn’t really understand it all. I am a very visual learner and I still don’t exactly know what his answer or way of thinking was but I knew it was one step further than where I still was so I tried to attempt thinking of was I could speed up the process and maybe create an equation. But I got stumped, I couldn’t figure out a way to account for every box in the 8x8 in a equation. Until I got to have a discussion with Dominic about everything I didn’t understand. And how it was much more efficient for me to start from the 8x8 squares down to 7x7 etc. And I noticed the pattern that x2+(x-12 )... and that all together it equals 204.
Reflection: I learned a lot from this problem about not giving up and collaboration. Two of the habits of a mathematician I used while working on this problem was Collaborate and Listen and Be confident, Patient and Persistent. Because even when I got stumped and I couldn’t figure it out I persevered and got help from my peers when I needed it and listened. Being patient and persistent is really what helped me finish this problem and feel confident afterwards in my understanding from the help of my peers.