Explanation of SET Functioning
In 1974, a pattern-recognition card game named SET made its debut, and since then, hundreds of thousands of copies have been sold worldwide, making it a global phenomenon. This game, initially designed for data visualization in population geneticist research, has evolved into an engaging and intellectually stimulating pastime.
SET is a game that can be played on smartphones and iPads, as well as with physical cards. The objective is simple yet challenging: to make a SET of three cards that either share a common feature (shape, color, shade, or number) or have no common feature at all. If a player finds a SET, they point it out, and the SET is removed, with three new cards added from the deck.
The mathematical structure of SET is rooted in set theory, abstract algebra, and finite geometry. Each card is represented as a vector in a 4-dimensional space over the finite field with 3 elements, known as (\mathbb{Z}_3^4). Three cards form a "set" when their corresponding vectors sum to the zero vector modulo 3, meaning that for each feature, the values are either all the same or all different.
This intricate mathematical framework allows SET to be studied using methods from combinatorics, linear algebra, and group theory, linking the gameplay directly to structures studied in pure mathematics. Sets of cards correspond to arithmetic progressions in this vector space, tying the game to group theory concepts.
SET is not just a game; it's a mental workout, whether players realize it or not. It encourages concentration, pattern recognition, quick-thinking skills, and even stimulates connections between the right and left sides of the brain. It's no surprise that SET is used in classrooms from elementary through high school to help students sharpen their thinking skills.
SET tournaments are held, and the New York Times publishes an online multiplayer version daily. Multiple people can play SET simultaneously, and the game continues until the deck of 81 cards is depleted and all possible SETs are made. If a SET cannot be made, three more cards are added. A SET is not valid if two cards share a common feature and one does not.
To determine a winner among multiple players, one point is awarded per SET found (and one may be subtracted for each invalid SET pointed out); the player with the most points at the end of the game wins. With its engaging gameplay and cognitive benefits, it's no wonder SET has captured the hearts and minds of players for over four decades.
References:
[1] Conway, J. H., Linton, S. J., Smith, D. E., & Wilson, R. A. (2008). The Symmetries of Things. Springer Science & Business Media.
[3] Graham, R. L., Knuth, D. E., & Patashnik, O. (1994). Concrete Mathematics: A Foundation for Computer Science. Addison-Wesley.
This intellectual card game, SET, can be played on smartphones and tablets, demonstrating the integration of traditional games with modern technology. The game's mathematical structure, rooted in set theory, abstract algebra, and finite geometry, showcases its connection to advanced concepts in technology and mathematics, making it a fascinating bridge between recreation and academia.
