Gardner, Martin: Mathematical Puzzles & Diversions ©1959 Martin Gardner Simon & Schuster, NY Softcover, perfect-bound, 5.5x8.5", 179 pages ISBN: 0-671-63652-9 Also in Hardcover

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Comments: "Scientific American Book of" Material previously published in Scientific American is copyright 1956, 1957, 1958 by Scientific American. Includes a chapter on Mathematical Magic with Cards.

Contents (from book):

ix Introduction (Martin Gardner)
1 Hexaflexagons: folded paper polygons with property of changes faces when flexed; with applications
8 Addendum: construction tips, coloring, letters

15 Magic With a Matrix: Magic Squares
21 Addendum: letter variation by Stewart James

23 Nine Problems
23 The Returning Explorer
23 Draw Poker
24 The Mutilated Chess Board
25 The Fox in the Road
25 Scrambled Box Tops
25 Bronx vs. Brooklyn
26 Cutting the Cube
26 The Early Commuter
26 The Counterfeit Coins
27 Answers

37 Ticktacktoe
37 Introduction
38 The Basic Play
39 More Mathematically Exciting Versions
41 Go-Moku
43 Robots
45 Addendum: spelling and pronunciation, taking advantage of a bad play

47 Probability Paradoxes: Unexpected Probabilities
47 Shared Birthdays
49 Getting an Ace
51 The Second Child
51 St. Petersburg Paradox
52 Hempel's Paradox

55 The Icosian Game and the Tower of Hanoi
55 The Icosian Game
57 The Tower of Hanoi
59 How They Are Related
60 Addendum

63 Curious Topological Models
63 Moebius Band
64 The Double Mobius Band
66 Tuckerman's Model
67 List of Curious Topologial Models
71 Addendum: plastic model of a double Moebius band

73 The Game of Hex: invented by Piet Hein
73 How It Is Played
74 Hex Invention
75 Tips to Play: and different sized boards
77 The Winning Strategy
78 Variations
78 Addendum
82 - Answers

84 Sam Loyd - America's Greatest Puzzlist
84 Some History
85 Loyds Chess Problem
86 P.T. Barnum's Trick Donkeys
87 The 15-15 or Boss Puzzle
88 Rate Your Mind Pal: variation
89 Get Off the Earth Paradox: visual puzzle and variation
89 Kingfish vs. Devilfish
92 Addendum
93 Answers

96 Mathematical Card Tricks
96 Reversed Coincidence: magician turns cards face up under table to match number of face up cards in spectator's packet
99 Speller: random name spells to the selection
100 Card Prediction: spectator deals cards as instructed and selected card matches prediction
101 Some Card Odds

102 Memorizing Numbers
103 Using Mnemonics
104 Rhymes to Memorize Numbers
104 The Number Alphabet: to memorize any number sequence
106 Using the Number Alphabet for Square Roots
108 Mental Pictures
109 Addendum

110 Nine More Problems
110 The Touching Cigarettes
111 Two Ferry Boats
111 Guess The Diagonal
111 The Efficient Electrician
112 Cross the Network
112 The Twelve Matches
113 Hole In the Sphere
113 The Amorous Bugs
114 How Many Children?
114 Answers

124 Polyominoes
124 Simply Connected Set of Squares
127 Henry Dudeney's Problem
131 The Triplication Problem (Raphael M. Robinson)
131 Other Problems
133 Pentomino Game
139 Addendum

141 Fallacies
141 Flawed Mathematical Proofs
142 The Ten Travellers
143 Any Number a Equal to Smaller Number b
144 Imaginary Number Proof
144 Geometric Fallacy The Curry Triangle
146 The Expensive Tie
146 Torus Paradox
148 Interesting and Uninteresting Numbers
148 Addendum

151 Nim and Tac Tix
151 Nim
152 Safe and Unsafe Plays
156 Computers and Nim
156 Variations of Nim
157 Tac Tix (Piet Hein): variation
159 Addendum
161 - Answers

163 Left or Right?
163 Handedness of Fundamental Particles
163 Mirrors and Symmetry
164 Musical Reflection
165 Figure Refelection
166 Word Reflection
167 Three Dimensional Reflection
170 Addendum: why does a mirror reverse left and right but not up and down?

174 References for Further Reading
174 Hexaflexagons
174 Magic With a Matrix
174 Tictacktoe
175 Probability Paradoxes
176 The Icosian Game and the Tower of Hanoi
176 Curious Topologial Models
176 Sam Loyd America's Greatest Puzzlist
176 Mathematical Card Tricks
177 Memorizing Numbers
177 Polyominoes
177 Falacies
177 Nim and Tac Tix
178 Left or Right
179 About the Author