"But Grant, the Putnam's not really the hardest test, and if you really want to find the hardest problem..."
Yeah, yeah, of course. But if having an imprecise-but-not-totally-off-base title means this lesson reaches more people, great!
For one thing, it's just a very elegant solution well worth sharing. But I'm always fascinated by the question of how one would find elegant solutions that just look like they were plucked out of thin air. That is, rather than perpetuating the illusion of innate genius by just showing the solution, try shedding some light on what background/tactics might lead someone to the relevant insight.
More often than not, the answer has more to do with someone's past experiences than with the problem-solving techniques they used in the moment of the puzzle. But every now and then there actually is a lesson to be taken away in terms of how you might systematically expose yourself to interesting insights, and the goal of this video is to share one such lesson.