The video is not so much about the problem solving process so it's not good for hints. The visualizations alone makes the problem a lot easier off the bat.

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!

The problem:

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.

if not all points in P are coplanar then what does it mean to rotate clockwise? perpendicular to which axis?

They are all coplanar, but no three points are colinear. The first sentence just means that there are at least 2 points in the set.

The start of the video is talks about the problem and illustrates some concrete examples. At 6:50 it starts the solution, by presenting a key invariant.

There's maybe a step or two's worth of that, then the answer. The video is not explicitly structured as a set of clues, it only accidentally half-does that because it builds up to the answer mathematically, but I would not say the steps are "even" in size.

is this in essence a convex-hull problem, except instead of closing, we continue?

I think he presents a line of reasoning that also helps to formalize why finding a convex hull works.

I don't think so. In a convex hull, you only visit points on the hull of the set, not in the interior. In this problem, you visit points in the interior too (if I understand correctly).

You get to choose the line so that this circuit is possible. If you didn’t, you’d essentially be able to form a convex hull and thus not visit all the points.

No. In fact, in the end he shows a list of approaches one might think are related but turn out not to be, and computing convex hulls is one of them.

Grant Sanderson manages to combine his compelling narrative style with elegant animations. The solution to the chosen puzzle only depends on very straightforward mathematical knowledge. Grant shows a possible route towards discovering the invariants that rule this puzzle.

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.

You can obtain the problem statement on this page: https://www.imo-official.org/problems.aspx