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, 2017. All Rights Reserved. Under the terms of the licence agreement, an individual user may print out a PDF of a single chapter of a monograph in HSO for personal use (for details see http://www.universitypressscholarship.com/page/privacy-policy).date: 22 January 2018

Tic-tac-toe on Affine Planes

Tic-tac-toe on Affine Planes

Chapter:
13 Tic-tac-toe on Affine Planes
Source:
The Mathematics of Various Entertaining Subjects
Author(s):

Maureen T. Carroll

Steven T. Dougherty

Publisher:
Princeton University Press
DOI:10.23943/princeton/9780691164038.003.0013

This chapter introduces a new game of tic-tac-toe that fits squarely within the body of work inspired by mathematician Leonhard Euler's findings on the so-called “Graeco-Latin squares” and the surprisingly interesting problem of arranging thirty-six officers of six different ranks and regiments. In his 1782 paper on the subject, Euler begins with the thirty-six-officer problem and ends with a conjecture about the possible sizes of Graeco-Latin squares. The chapter first explains the rules for a game based on Euler's work, and then analyzes it from a game-theoretic perspective to determine winning and drawing strategies. Along the way, the chapter explains Euler's connection to the story.

Keywords:   tic-tac-toe, affine planes, Leonhard Euler, Graeco-Latin squares, game-theoretic perspective, winning strategies

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.