I didn't find the video, I'd be interested in seeing it too. But I did find this: https://www.cs.stanford.edu/~knuth/papers/cs1055.pdf It's a set of notes of a problem solving seminar that Knuth taught to grad students at Stanford in 1985. It looks interesting.
I'm also curious to see this. I think a lot of the really strong programmers I know do this instinctually where as I have to be more deliberate breaking things down. Perhaps some of it is that they are able more more naturally hold it in their minds than writing it out on a piece of paper like I do. Maybe they "learned how to learn" in that way better than I did when they were younger.
At one point around 20 or 30 minutes in, he says something like, “We’re going to start easy and slow and then work harder later on.” He exhaustively writes out a large number of different combinations of possible runtimes of an algorithm. It seems quite tedious, but eventually some cool results emerge related to Sterling Numbers :)
At first, I thought it was somewhat annoying that the lecture was methodically going through so many examples. Since then, I’ve realized that methodically going through small sub-problems patiently is often the way you eventually get to a giant leap.