Goodbye (CSC104) World!

It's the final week of school! Well, final week of classes. This will be my final post for this "SLOG". It's been a busy semester but I made it through! Project 2 is complete (I hope I do better on this one...) and now this blog is also complete. Now, all that's left to do is provide a solution to a problem that I encountered during this course.

So at the beginning of the semester, the professor asked us to determine an "algorithm" for the number of ups and downs you get on a piece of paper after every time you fold the paper in half. The first fold you get one down (D). The second fold you get up (U) D D. The third fold you get UUDDUDD. The fourth fold gives UUDUUDDDUUDDUDD. This looks pretty confusing but there is a trend. To show this, you can rewrite the third and fourth folds as U U D D U D D and UUD U UDD D UUD D UDD. From this, you can see that there is a constant D in the middle and a constant U and D that "surrounds" the D in the middle (second fold: U D D). So, for n=3 folds, you take the surrounding U and D surrounding the middle D and use those to surround both of them: UUD D UDD. For n=4, you repeat the steps for n=3: take the ups and downs surrounding the middle D and use those to surround the constant U and D. This becomes UUDUUDD D UUDDUDD. Hence, you can make an algorithm for this: For n > 2, where n represents the number of folds, you add the ups and downs surrounding the central down fold of n-1 to either side of the up and down folds found in n = 2.

Hm...that algorithm sounds pretty confusing. Not sure how else to say it though! Well, hopefully you guys understand it...

Anyway, hope everyone's doing well and good luck on all your exams! That's all from me. Goodbye!