The code I'm most proudest of is that which solves a problem I thought would be unsolvable, with which I tried using several different methods, to then eventual

The code I'm most proudest of is that which solves a problem I thought would be unsolvable, with which I tried using several different methods, to then eventually settle on a final design, probably a compromise between readability and efficiency. I think you should give them code that tells a story. One with comments which explain why you did A and not B. Write an accompaniment to it "At first, I tried A. I researched and found out X, but...". Few people can discover something as incredible as FFT, or FISR. Those are one-offs. It shows a lot if you worked hard at getting a solution to a problem and that you're proud of it; you didn't just copy-paste, you tried different ways of solving it and ended up with a solution that's, in the words of Goldilocks, just right. Or that's what I'd send them at least.