The Mathematics of Games and Puzzles: From Cards to …

Topic Science & Mathematics

Subtopic Mathematics

The Mathematics of Games and Puzzles: From Cards to Sudoku

Course Guidebook

Professor Arthur T. Benjamin

Harvey Mudd College

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Arthur T. Benjamin, Ph.D. Professor of Mathematics Harvey Mudd College

Professor Arthur T. Benjamin is a Professor of Mathematics at Harvey Mudd College. In 1983, he graduated from Carnegie Mellon University, earning his B.S. in Applied Mathematics with university honors. In 1989, he received his Ph.D. in Mathematical Sciences from Johns Hopkins University, where he was supported by a National Science Foundation graduate fellowship and a Rufus P. Isaacs fellowship. Since 1989, Professor Benjamin has been a faculty member of the Department of Mathematics at Harvey Mudd College, where he has served as Department Chair. He has spent sabbatical visits at the California Institute of Technology; Brandeis University; the University of New South Wales in Sydney, Australia; and the University of Oxford.

In 1999, Professor Benjamin received the Southern California-Nevada Section Award for Distinguished College or University Teaching of Mathematics from the Mathematical Association of America (MAA), and in 2000, he received the MAA's national Deborah and Franklin Tepper Haimo Award for Distinguished College or University Teaching of Mathematics. He was also named the 2006?2008 George P?lya Lecturer by the MAA. Professor Benjamin was chosen by The Princeton Review as one of its Best 300 Professors. In 2012, he was selected as an inaugural Fellow of the American Mathematical Society. Professor Benjamin has given widereaching TED talks, one of which has been viewed more than five million times. In 2005, Reader's Digest named him "America's Best Math Whiz." An avid game player, Professor Benjamin is a previous winner of the American Backgammon Tour.

Professor Benjamin's research interests include combinatorics, game theory, and number theory, with a special fondness for Fibonacci numbers. Many of these ideas appear in his book (coauthored with Jennifer Quinn) Proofs

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That Really Count: The Art of Combinatorial Proof, published by the MAA. In 2006, Proofs That Really Count received the MAA's Beckenbach Book Prize. From 2004 to 2008, Professors Benjamin and Quinn served as the coeditors of Math Horizons magazine, which is published by the MAA and enjoyed by more than 20,000 readers, mostly undergraduate math students and their teachers. In 2009, the MAA published Professor Benjamin's latest book, Biscuits of Number Theory, coedited with Ezra Brown.

Professor Benjamin is also a professional magician. He has given thousands of "mathemagics" shows in venues around the world, from primary schools to scientific conferences, in which he demonstrates and explains his calculating talents. His techniques are explained in his book Secrets of Mental Math: The Mathemagician's Guide to Lightning Calculation and Amazing Math Tricks. Prolific math and science writer Martin Gardner called the book "the clearest, simplest, most entertaining, and best book yet on the art of calculating in your head."

Professor Benjamin has appeared on dozens of television and radio programs, including the TODAY show and The Colbert Report as well as CNN and National Public Radio. He has been featured in Scientific American, Omni, Discover, People, Esquire, The New York Times, the Los Angeles Times, and Reader's Digest.

Professor Benjamin has taught three other Great Courses: The Joy of Mathematics, Discrete Mathematics, and The Secrets of Mental Math.

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Table of Contents

INTRODUCTION

Professor Biography ............................................................................i Course Scope.....................................................................................1

LECTURE GUIDES

LECTURE 1 Let the Games Begin!.........................................................................4 LECTURE 2 Games of Chance and Winning Wagers .......................................... 11 LECTURE 3 Optimal Blackjack and Simple Card Counting..................................18 LECTURE 4 Mixed Strategies and the Art of Bluffing ...........................................26 LECTURE 5 Practical Poker Probabilities.............................................................34 LECTURE 6 Expert Backgammon ........................................................................43 LECTURE 7 Games You Can't Lose and Sneaky Puzzles ...................................51 LECTURE 8 Solving "Impossible" Puzzles............................................................59 LECTURE 9 Mastering Rubik's Cube ...................................................................70 LECTURE 10 Solving Sudoku.................................................................................78

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