How to Make "Trick Dice" That Are Actually Fair

This video was sponsored by Brilliant! Check out https://brilliant.org/PurpleMind/ for a 30-day free trial and a 20% discount on an annual premium subscription.

This is episode "2B" 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.
-- In the second part, I follow up with animated discussions of the solutions that were sent to me, mixed in with my own thoughts.

This one is about relabeling the numbers on dice to get a rather interesting property. (https://en.wikipedia.org/wiki/Sicherm...)

Thanks so much to Brilliant for being the first sponsor of this channel, to everyone who submitted something for this problem, and to everyone, in general, for watching the video!
Also, special thanks to PolyaMath for sending in such a detailed animation of his solution (9:06). He makes really awesome videos on YouTube and you should definitely check him out if you enjoy the content on this channel:    / @polyamathematics  .

Part 1:    • Dice Don't Normally Look Like This...  

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These animations are made using Manim, by 3Blue1Brown.