2018-03-15

[public] 49.6K views, 1.41K likes, 55.0 dislikes audio only

PBS Infinite Series

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In the card game SET, what is the maximum number of cards you can deal that might not contain a SET?

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Resources

Official SET game instructions

https://www.setgame.com/sites/default/files/instructions/SET%20INSTRUCTIONS%20-%20ENGLISH.pdf

Simple SET Game Proof Stuns Mathematicians (Quanta Magazine)

https://www.quantamagazine.org/set-proof-stuns-mathematicians-20160531/

The Problem with SET (NYTimes Puzzle)

https://www.nytimes.com/2016/08/22/crosswords/the-problem-with-set.html

Open Question: Best Bounds for Cap Sets (blog post by Terry Tao)

https://terrytao.wordpress.com/2007/02/23/open-question-best-bounds-for-cap-sets/

SET and Group Theory by Pavel Etingof (see p. 13ff)

http://www-math.mit.edu/~etingof/groups.pdf

This episodes challenge question is: Among the 9 cards shown in this episode what is the maximum number of them that may not contain a SET? Can you rephrase this question in an equivalent yet geometric way and then answer it using the hint - SETs correspond to lines in the Z/3Z grid?

Email your answers to pbsinfiniteseries@gmail.com with the subject line "SET Challenge" along with your proof. A random winner will be selected among the submissions to win a PBS Digital t-shirt.

(Spoiler Alert!) Here's the solution to the SET challenge problem: https://bit.ly/2Ggpw1d

Previous Episode:

What was Fermat’s “Marvelous" Proof?

/youtube/video/SsVl7_R2MvI

Let's talk about the card game SET. To play, you start with a deck of cards, each of which has a certain number of shapes in different colors and shadings. You deal out 12 cards and start looking for a SET---a collection of 3 cards that have either all the same or all different patterns. Now, once you deal those 12 cards, it’s possible that there might not be a SET among them. When that happens, you just deal out 3 more cards. And… in some cases, there still might not be a SET. So… you can add 3 more cards. And this begs the question: What is the maximum number of cards you can deal that might not contain a SET?

Written and Hosted by Tai-Danae Bradley

Produced by Rusty Ward

Graphics by Ray Lux

Assistant Editing and Sound Design by Mike Petrow and Linda Huang

Made by Kornhaber Brown (www.kornhaberbrown.com)

Special thanks to Roman Pinchuk for supporting us on our Converse level on Patreon.

Along with thanks to Matthew O'Connor, Yana Chernobilsky, and John Hoffman who are supporting us on Patreon at the Identity level!

And thanks to Mauricio Pacheco and Andrew Poelstra who are supporting us at the Lemma level!