That Project Euler problem was my first encounter with memoization. At the time, it felt like a magical solution, so I ended up solving it using the central column of Pascal's triangle, which was easier for me to understand back then.

I also tried a weird idea involving popcount, but it didn't scale. My approach was to represent each possible path with 0s (don't turn) and 1s (turn), testing the same number of 0s and 1s. However, even with popcount running in O(1) with hardware support, the total number of possible paths made the idea impractical :)