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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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Tic-tac-toe on Affine Planes

Tic-tac-toe on Affine Planes

13 Tic-tac-toe on Affine Planes
The Mathematics of Various Entertaining Subjects

Maureen T. Carroll

Steven T. Dougherty

Princeton University Press

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

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