SET! From Groups to Games

TL;DR

This paper explores mathematical generalizations of the game SET, focusing on group theory and arithmetic progressions, and discusses factors affecting the game's enjoyment.

Contribution

It introduces and analyzes new generalizations of SET based on group multiplication and arithmetic progressions, expanding the mathematical understanding of the game.

Findings

Generalizations involve sets multiplying to identity

Sets forming arithmetic progressions are studied

Game properties influencing enjoyment are discussed

Abstract

The game of SET is one of the best mathematical games ever. It is no wonder that people have tried to generalize it. We discuss existing generalizations of the game of SET to different groups. We concentrate on two types of generalization: a) where a set consists of cards that multiply to the identity; b) where a set consists of three cards that form an arithmetic progression. We finish with a discussion of some properties of the games that influence how enjoyable they are.