Winning Ways for Your Mathematical Plays

✍ Scribed by Elwyn R. Berlekamp, John H. Conway, Richard K. Guy

• Publisher: A K Peters/CRC Press
• Year: 2004
• Tongue: English
• Leaves: 181
• Series: AK Peters/CRC Recreational Mathematics Series
• Edition: 2
• Category: Library

✦ Synopsis

In the quarter of a century since three mathematicians and game theorists collaborated to create Winning Ways for Your Mathematical Plays, the book has become the definitive work on the subject of mathematical games. Now carefully revised and broken down into four volumes to accommodate new developments, the Second Edition retains the original's wealth of wit and wisdom. The authors' insightful strategies, blended with their witty and irreverent style, make reading a profitable pleasure. In Volume 4, the authors present a Diamond of a find, covering one-player games such as Solitaire.

✦ Table of Contents

Cover
Half Title
Title Page
Copyright Page
Contents
Dedication
Preface to the Second Edition
Preface to the Original Edition
23 Purging Pegs Properly
Central Solitaire
Dudeney, Bergholt and Beasley
Packages and Purges
Packages Provide Perfect Panacea
The Rule of Two and the Rule of Three
Some Pegs AreMore Equal Than Others
Reiss’s 16 Solitaire Position Classes
The Continental Board
Playing Backwards and Forwards
Pagoda Functons
The Solitaire Army
Managing Your Resources
Unproductivity and the Prodigal Son
Deficit Accounting and the G.N.P
Accounting for Two-Peg Reversal Problems
Forgetting the Order Can Be Useful
Beasley’s Exit Theorems
A Stolid Survivor Problem
Another Hard Problem
The Spinner
Our Fine Finalist
Doing the Splits
All Soluble One-Peg Problems on the Continental Board
The Last Two Moves
A 20-Man Solitaire Army
Fool’s Solitaire, Etc
Beasley Proves Bergholt Is Best
The Classical Problems
References and Further Reading
24 Pursuing Puzzles Purposefully
Soma
Blocks-in-a-Box
Hidden Secrets
The Hidden Secrets of Soma
Hoffman’s Arithmetico-Geometric Puzzle
Coloring Three-by-Threee-by-Three by Three, Bar Three
Wire and String Puzzles
The Magic Mirror Method
The Barmy Braid
The Artful Arrow
The Magic Movie Method
Party Tricks and Chinese Rings
Chinese Rings and the Gray Code
The Tower of Hano
A Solitaire-Like Puzzle and Some Coin-Sliding Problems
The Fifteen Puzzle and the Lucky Seven Puzzle
All Other Courses for Point-to-Point
The Hungarian Cube-Buvos Kocka
Just How Chaotic Can the Cube Get?
Chief Colors and Chief Faces
Curing the Cube
A: Aloft, Around (Adjust) and About
B: Bottom Layer Corner Cubelets
C: Central Layer Edge Cubelets
D: Domiciling the Top Edge Cubelets
E: Exchanging Pairs of Top Corners
F: Finishing Flips and Fiddles
Explanations
Improvements
Elena’s Elements
Are You Partial to Partial Puzzles?
Other “Hungarian” Objects
A Trio of Sliding Block Puzzles
Tactics for Solving Such Puzzles
Counting YourMoves
Paradoxical Pennies
Paradoxical Dice
More on Magic Squares
The Magic Tesseract
Adams’s Amazing Magic Hexagon
The Great Tantalizer
Polyominoes, Polyiamonds and Searching Policy
Alan Schoen’s Cyclotome
Macmahon’s Superdominoes
Quitominal Dodecahedra
The Doomsday Rule
...and Easter Easily
How Old is the Moon?
Jewish New Year (Rosh Hashana)
Blocks-in-a-Box
The Somap
Solutions to the Arithmetico-Geometric Puzzle
...and One for “Three” Too!
Hares and Tortoises
The Lucky Seven Puzzle
Top Face Alterations for the Hungarian Cube
The Century Puzzle
Adams’s Amazing Magic Hexagon
Flags of the Allies Solution
All Hexiamond Solutions Found
The Three Quintominal Dodecahedra
Answer to Exercise for Experts
Where Do the Black Edges of Magmahon Squares Go?
Doomsday Answers
References and Further Reading
25 What is Life?
Still Life
Life Cycles
The Glider and Other Space Ships
The Unpredictability of Life
Gardens of Eden
Life’s Problems are Hard!
Making a Life Computer
When Glider Meets Glider
How to Make a not Gate
The Eater
Gliders Can Build Their Own Guns!
The Kickback Reaction
Thinning a Glider Stream
Building Blocks for Our Computer
Auxiliary Storage
How We Move Blocks
A Little Difficulty
Mission Completed–Will Self-Destruct
Life Computers Can Reproduce!
Genetic Engineering
Whither Life?
References and Further Reading