Since this is a puzzle that will certainly nerd-snipe a number of us, could someone who already watched the video tell us if there is a "spoiler" moment in it or if we could watch it bit by bit in case that we get stuck?
It's mainly about showcasing a problem that is objectively hard (based on IMO competition results) then revealing the simple thought process that will lead you to an "obvious" answer in a few short minutes. The main point is that there are problems where once you know the "trick", you can't accurately judge how hard the problem is anymore.
I think people would appreciate that point a lot more if they struggle with the problem for a bit first!
Let S be a finite set of at least two points in the plane. Assume that no three points of S are collinear. By a windmill we mean a process as follows. Start with a line l going through a point P ∈ S. Rotate l clockwise around the pivot P until the line contains another point Q of S. The point Q now takes over as the new pivot. This process continues indefinitely, with the pivot always being a point from S.
Show that for a suitable P ∈ S and a suitable starting line l containing P, the resulting windmill will visit each point of S as a pivot infinitely often.
It is a kind of puzzle to try out on your own, knowing that a rather simple mathematical reasoning solves it. It doesn't rely on some obscure mathematical knowledge as might be suspected from an Olympiad problem.
If you want to see Grant Sanderson, instead of only hearing his voice, he uploaded a Q&A where he explains his motivations. Mainly, creating educational math videos that other people would not be able to create.