The Joy of Set


Some Combinatorial Questions Related to the

Configuration of Points in Z_3^k

Mike Zabrocki
York University


The official web page for the game of Set® can be found at .  This site has information on how to obtain the card game, rules of the game, links to other web sites with information about the game, some mathematics and some trivia.

Advanced Set

Play the game here

I have written a Java version of the card game that can be played within a web page here that should work on Internet Explorer with a reasonably updated version of Java or downloaded in zip format for Macintosh OS 9 (or earlier?...It should just activate Apple Applet Runner).  Other platforms may download the source in .tar.gz format and modify it so that it works on their system.

The Joy of Set

There is also an html and pdf version of a document that explains the game of set, the extended version that I have written here, and some mathematics that is associated with the game.  This pdf document along with the program was written to be presented at FPSAC '01 at Arizona State University in May, 2001. Feel free to contact me and comment about this document. The following changes need to be added if I were to ever update the paper.

The open problem number 1 that is in this document is not really open. Diane Maclagan showed me a proof at FPSAC '01. I didn't come up with a solution when I was writing the paper so I pegged it for "very hard" when it was really somewhere between "not obvious" and "difficult." I have also received other nice solutions from people who e-mailed me. The answer is (from one of the last e-mails I received)

|I_k|=3^k * Product for i from 0 to k-1 of (3^k-3^i)

Also, the maximal number of cards with no set is called 'a maximal cap in A(3,n)' where n is the number of properties. I did not know that this language when I first wrote this. The size of a maximal cap of A(3,n) for n equal to 1 through 5 is 2, 4, 9, 20, 45. I believe that the answer is currently not known for n=6 but that it is known to be between 111 and 115. Computationally this question is hard.

Diane Maclagan and Bejamin Davis have written a paper for The Mathematical Intelligencer about the Game of Set.
Check out the an article by Ivars Peterson.
Some other links:
Observations on the game of set
The SET® Home Page.

I would like to thank Andrew Rechnitzer for helpful suggestions and encouragement.  I would also like to thank Carol Chang, Murray Elder, Nantel Bergeron, John Wild, and Jamal Ahmed for their advice, support, equipment use and suggestions.

Home page of Mike Zabrocki

email: zabrocki(at)mathstat(dot)yorku(point)ca