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The Mathematics of Various Entertaining SubjectsResearch in Recreational Math$
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Jennifer Beineke and Jason Rosenhouse

Print publication date: 2015

Print ISBN-13: 9780691164038

Published to Princeton Scholarship Online: October 2017

DOI: 10.23943/princeton/9780691164038.001.0001

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Error Detection and Correction using SET®

Error Detection and Correction using SET®

Chapter:
(p.199) 14 Error Detection and Correction using SET®
Source:
The Mathematics of Various Entertaining Subjects
Author(s):

Gary Gordon

Elizabeth McMahon

Publisher:
Princeton University Press
DOI:10.23943/princeton/9780691164038.003.0014

This chapter considers two fundamental questions for detecting and correcting errors made while playing the card game SET®. The game is played with a special deck of eighty-one cards, and the objective is to find three cards that form a set. Over the course of a game, a player may make a mistake by taking three cards that do not form a set—a common occurrence which this chapter examines by first introducing coordinates for the cards and then uses these coordinates to define a Hamming weight for any subset of cards. The chapter then uses the facts about Hamming weight to describe a variant of the game, called the EndGame, which leads to error detection. Afterward, the chapter produces a perfect, single-error-correcting linear code solely from SET® cards. It concludes with additional topics that demonstrate the deep connections between the simple card game and advanced mathematics.

Keywords:   SET, error detection, card games, Hamming weight, EndGame, linear code, advanced mathematics, error correction, coding theory

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