Simple Set Game Proof Stuns Mathematicians

Dear gods, I hate these stupid clickbait titles... but that's what the title says. Mathematicians were NOT stunned. Interested, yes. Fascinated, yes. Ran off to find the equations and play with them, yes.

But not stunned like electrocuted goldfish.

In a series of papers posted online in recent weeks, mathematicians have solved a problem about the pattern-matching card game Set that predates the game itself. The solution, whose simplicity has stunned mathematicians, is already leading to advances in other combinatorics problems.

Invented in 1974, Set has a simple goal: to find special triples called “sets” within a deck of 81 cards. Each card displays a different design with four attributes — color (which can be red, purple or green), shape (oval, diamond or squiggle), shading (solid, striped or outlined) and number (one, two or three copies of the shape). In typical play, 12 cards are placed face-up and the players search for a set: three cards whose designs, for each attribute, are either all the same or all different.

Occasionally, there’s no set to be found among the 12 cards, so the players add three more cards. Even less frequently, there’s still no set to be found among the 15 cards. How big, one might wonder, is the largest collection of cards that contains no set?

Source [url=https://www.quantamagazine.org/20160531-set-proof-stuns-mathematicians/]https://www.quantamagazine.org/20160531-set-proof-stuns-mathematicians/[/ url]

It's surprisingly readable and actually very interesting.

I liked the conclusion:

The fact that the cap set problem finally yielded to such a simple technique is humbling, Ellenberg said. “It makes you wonder what else is actually easy.”

www.quantamagazine.org...

how cool....

like with the game rummycub....once 5/8 of the tiles are out on the board....I can always run the table completely....

originally posted by: GBP/JPY
how cool....

like with the game rummycub....once 5/8 of the tiles are out on the board....I can always run the table completely....

Interesting! I am sure there's a mathematical strategy there (but I don't know enough math to suggest what it might be.)