Can You Solve This Geometric Puzzle?

This is episode 3 in a series called "Brainstorm."

The topics for these videos are puzzle-style problems, broken into two parts each, a couple months apart.
-- In the first part, I introduce the problem, and you (the viewers) try to solve the problem yourself, or at least come up with some initial approaches or first steps. I encourage you all to submit your (possibly partial) solutions to me through the Google Form (forms.gle/D16AskjnxP9cMVpJ9) before 11/14/2024!
-- In the second part, I follow up with animated discussions of the solutions that were sent to me, along with my own solution.
You can check out the latest follow-up episodes here:
   • How to Make "Trick Dice" That Are Actually...  
   • My Viewers Are Math Geniuses  

This one is about a certain randomized iterative process that one can use to create a very pretty geometric construct called a Voronoi Diagram (named after Georgy Voronoi).

Have fun, and I look forward to seeing what you all come up with!

Puzzle #1:    • Coin-flipping puzzle (I dare you to solve it)  
Puzzle #2:    • Dice Don't Normally Look Like This...  

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These animations are made using Manim, by 3Blue1Brown.