Jump to ContentJump to Main Navigation
The Mathematics of Various Entertaining SubjectsResearch in Recreational Math$
Users without a subscription are not able to see the full content.

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

Show Summary Details
Page of

PRINTED FROM PRINCETON SCHOLARSHIP ONLINE (www.princeton.universitypressscholarship.com). (c) Copyright Princeton University Press, 2021. All Rights Reserved. An individual user may print out a PDF of a single chapter of a monograph in PRSO for personal use.date: 19 September 2021

Error Detection and Correction using SET®

Error Detection and Correction using SET®

(p.199) 14 Error Detection and Correction using SET®
The Mathematics of Various Entertaining Subjects

Gary Gordon

Elizabeth McMahon

Princeton University Press

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

Princeton Scholarship Online requires a subscription or purchase to access the full text of books within the service. Public users can however freely search the site and view the abstracts and keywords for each book and chapter.

Please, subscribe or login to access full text content.

If you think you should have access to this title, please contact your librarian.

To troubleshoot, please check our FAQs , and if you can't find the answer there, please contact us.