We solve a cute problem about acute triangles from the 1970 International Math Olympiad (Problem 6). We improve the 70% bound. We conclude with an open problem on the best bound.

00:00 Introduction
02:21 Four Points
06:12 Five Points
10:54 100 Points
12:51 Better Upper Bounds
19:30 Two Constructions with Many Acute Triangles
25:05 Open Problem on the Best Bound
26:01 Problem-Solving Takeaways

Addendum: After I posted the video, I realized that the 2/3 upper bound can be improved quite a bit by using known results in extremal combinatorics. I may create a follow-up video with these improved bounds.

70% upper bound:
https://prase.cz/kalva/imo/isoln/isol...

My 2/3 upper bound (see the two posts by "Ravi B"):
https://artofproblemsolving.com/commu...

1/4 construction (Wendel's theorem):
https://en.wikipedia.org/wiki/Wendel%...
https://www.cut-the-knot.org/m/Probab...

5/9 construction:
https://math.stackexchange.com/questi...

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