UMASS Online
92.419 Intro to Mathematica
Kenneth M. Levasseur
Department of Mathematical Sciences
University of Massachusetts Lowell
Lowell, MA 01852

Set, The Game

Subject

Mathematics, games

Topic

The game of Set involves a deck of 81 cards. Each card has one of three attributes as to their symbol, color, number, and filling.

Symbol attributes: diamond, oval and squiggle
Color attributes: red, green and purple
Number attributes: one, two and three
Filling attributes: filled in, outlined and striped

For example, one card has two red diamonds that are filled in with stripes.

Twelve of the cards are placed face-up on the table and the players try to identify a "set". A "set" consists of three cards that, for each attribute, are identical or different. The cards in the set are removed and replaced with more cards.

Reference(s)

Set - the family game of visual perception, Copyrite © 1988,1991 Marsha J. Falco.
The Set Web Page

Project Idea(s)

Identify sets from among a collection of cards. It's still not a trivial problem but could be interesting and a real challege to do the checking efficiently. Most likely you would want to represent cards by four numbers, one for each attribute. This would be the "data structure." Collections of cards could be generated randomly or entered by the user.

Display cards as in the real game using graphics objects. Create an interface so that humans can look at and identify sets and Mathematica can check their validity. Here, the computer wouldn't be doing the identification so it might be easier.

You could also combine the two ideas above.

Caution: If you make major progress on this one, you might want to contact Marsha Falco before distributing your materials outside of this course.

An open question that probably wouldn't be answered by Mathematica is what is the minimum number of cards that are neccessary to be guaranteed that a set will appear.

Prerequisite Mathematics

Discrete geometry and modular arithmetic would seem to be useful but not at a level that couldn't be learned as you go along.

Required Programming Level

Moderate. Keys would be identification of a good data structure for cards, design of an interface.

Key Words

Games, Combinatorics

Reviewer

K. M. Levasseur (Kenneth_Levasseur@uml.edu)