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.
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)
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.