Sharing My Journey of Determination in Problem-Solving
This repository is all about my determined efforts to solve a challenging problem, and the exhilarating moment when I finally cracked it.
To be honest, it took me a few days to solve it, which is a bit frustrating. But I was so fixated on finding the solution that I couldn't stop myself. I practically isolated myself, working on the problem day and night for three consecutive nights. Even when I was doing other things, my mind was still racing with new ideas to try.
This persistent approach helped me learn and implement new strategies, and I kept trying until I finally succeeded.
I invested a considerable amount of time in my pursuit of solving Project Euler Problem 246, which revolves around ellipses. Interestingly, the problem's concept is quite straightforward to grasp, akin to Goldbach's Conjecture and Bertrand's Postulate. Despite its apparent simplicity, translating the problem statement into a working program proved to be a challenging endeavor, consuming approximately four to five days of my effort. It's worth noting that I had previously attempted to solve this problem about two years ago. While I did manage to find a solution at that time, it was not a complete one. It only worked for relatively small numerical cases and did not account for exceptional scenarios.
I wouldn't describe the problem as inherently difficult; in fact, it possessed a certain elegance. However, I must confess that my initial approach lacked a solid mathematical foundation. I had primarily approached the problem programmatically. On the other hand, I also delved into the study of ellipses, but I overlooked a beautiful equation related to the orthoptics of ellipses.
I owe a debt of gratitude to Wikipedia, which led me to the α-isoptics equation, and to Wolfram Alpha, which provided a solution to the quartic equation, ultimately aiding me in solving this intriguing problem.