In this problem we were trying to find how long it would take to move 64 disks from one peg to another, assuming you moved at a rate of one disk per second. The disks are originally stacked on the peg to the left, in ascending order top to bottom. The rules are you can only move one disk at a time and you can’t place a larger disk on top of a smaller disk.
When we first started this problem, Nayeli told us that she had posed this question to her brother brother as they were driving home from school one day. Surprisingly, they were able to come up with an answer using only our phones(they would ask siri to multiply for us because the numbers were so big). But we had to restart all of her work because she did not remember where she had started. When we wrote everything down, we were able to summarize the expanding difference between the number of moves it took to win based on the number of disks. This was, when there were 2 tiles, the next time it would take 2^2 more moves next time to win. And then when there were 3 tiles, the next time it would take 2^3 more moves next time to win. This could be summarized by the equation 2^D=M, where D represents the number of disks and M is the number of moves. To solve this problem, we simply substituted 64 where we had the number of disks.
When you take 2 to the 64th power, you get a huge number, which is the amount of moves you’ll have to make. To convert this into a more reasonable set of time, we turned it into years and got 584,942,417,355 years.
This problem was relatively simple. The pattern that I found was pretty straightforward. I think this problem is more of a warm up than a problem of the week. The solution is straightforward and simple, so this is definitely a problem I would do with the rest of the class just for fun.
I think I did very well on this problem, and believe it was an easy solution for me to find because I was able to relate it to other problems that I had previously solved in classes like challenge math and CS50.