The Classification of Magic SET Squares

TL;DR

This paper classifies all possible 3x3 magic SET squares under various transformations, calculates their counts per type, and explores a related SET tic-tac-toe game.

Contribution

It provides a comprehensive classification of magic SET squares and quantifies their distribution across different types, expanding understanding of SET square symmetries.

Findings

21 types of magic SET squares identified

Number of squares calculated for each type

Discussion of SET tic-tac-toe game included

Abstract

A magic SET square is a 3 by 3 table of SET cards such that each row, column, diagonal, and anti-diagonal is a set. We allow the following transformations of the square: shuffling features, shuffling values within the features, rotations and reflections of the square. Under these transformations, there are 21 types of magic SET squares. We calculate the number of squares of each type. In addition, we discuss a game of SET tic-tac-toe.