Hex: A Playful Introduction

142 Pages·2022·1.786 MB·English

by  Ryan B. Hayward

AMS / MAA ANNELI LAX NEW MATHEMATICAL LIBRARY VOL 54
Hex
A Playful Introduction
Ryan B. Hayward
Hex
A Playful Introduction
Ryan B. Hayward

AMS / MAA ANNELI LAX NEW MATHEMATICAL LIBRARY
VOL 54
Hex
A Playful Introduction
Ryan B. Hayward
Providence, Rhode Island
EDITORIAL COMMITTEE
John H. McCleary, Editor
Beth Malmskog
Tatiana Shubin
Thomas Q. Sibley
Bruce F. Torrence
Japheth Wood
2020 Mathematics Subject Classification. Primary 00A08, 00A09, 91A43,
91A27.
For additional informationand updates on this book, visit
www.ams.org/bookpages/nml-54
Library of Congress Cataloging-in-Publication Data
Names: Hayward,RyanB.,1958-author.
Title: Hex: aplayfulintroduction/RyanB.Hayward.
Description: Providence,RhodeIsland: AmericanMathematicalSociety,2022. |
Series: AnneliLaxnewmathematicallibrary,2578-6407;volume54|Includes
bibliographicalreferencesandindex.
Identifiers: LCCN2021049630|ISBN9781470464929(paperback)|9781470469481
(ebook)
Subjects: LCSH: Game theory. | Hex (Game) | Combinatorial analysis. | AMS:
General and overarching topics; collections – General and miscellaneous spe-
cifictopics–Recreationalmathematics. |Generalandoverarchingtopics;col-
lections–Generalandmiscellaneousspecifictopics–Popularizationofmath-
ematics. | Game theory, economics, finance, and other social and behavioral
sciences–Gametheory–Gamesinvolvinggraphs.
Classification: LCCQA269.H3882022|DDC519.3–dc23/eng/20211201
LCrecordavailableathttps://lccn.loc.gov/2021049630
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Do you like to play games?
This book is for you.

In memory
Fr´ed´eric Maffray (1960-2018),
graph theorist and friend;
Pouneh Gorji (1993-2020) and Arash Pourzarabi (1994-2020),
international scholars;
Audrey Jean Hayward (n´ee Banerd) (1934-2021),
quirky, funny, thoughtful, ever-curious, generous, loving.

contents
acknowledgments xiii
preface xv
1 this is Hex 1
1.1 rules 1
1.2 sample game 2
1.3 now it’s your turn 4
1.4 balancing the game 5
1.5 things to know 6
1.6 puzzles 7
1.7 solutions 8
2 basics 9
2.1 block 10
2.2 pairing 11
2.3 3×3 openings 12
2.4 safe connections 13
2.5 6×6 puzzle 14
2.6 win-threats 15
2.7 Fourth row safe connection 16
2.8 weak, safe, super connection 17
2.9 blunders 20
2.10 puzzles 22
2.11 solutions 23
3 how Hex began 25
3.1 Hein’s game 25
3.2 Lindhard’s puzzles 27
3.3 across the ocean 28
3.4 Gardner’s column and Nash’s lesson 28
3.5 puzzles 33
3.6 solutions 35
ix