The Geometry of SET | 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...

Simple SET Game Proof Stuns Mathematicians (Quanta Magazine)
https://www.quantamagazine.org/set-pr...

The Problem with SET (NYTimes Puzzle)
https://www.nytimes.com/2016/08/22/cr...

Open Question: Best Bounds for Cap Sets (blog post by Terry Tao)
https://terrytao.wordpress.com/2007/0...

SET and Group Theory by Pavel Etingof (see p. 13ff)
http://www-math.mit.edu/~etingof/grou...

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 [email protected] 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?
   • What was Fermat’s “Marvelous" Proof? ...  

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)

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