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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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Official SET game instructions
Simple SET Game Proof Stuns Mathematicians (Quanta Magazine)
The Problem with SET (NYTimes Puzzle)
Open Question: Best Bounds for Cap Sets (blog post by Terry Tao)
SET and Group Theory by Pavel Etingof (see p. 13ff)
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 firstname.lastname@example.org 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
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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