Math and Logic Games

Table of Contents
7 Introduction
9 Games with numbers
9 An historical note
11 A first curiosity
12 Fibonacci numbers
14 A curious calculating device: the abacus
20 The origins of algebra
21 Games with algebra
23 Odds and evens
24 The successor of a number
24 A shortcut in calculations
25 How much money is in your pocket?
25 How to guess a birth date
26 Guessing age and size of shoes
26 Where is the error?
27 Positional notation of numbers
28 One rotten apple can spoil the whole basket
29 Ordinary language and mathematical language
33 Games with geometrical figures
33 Geometry and optical illusions
41 Games with matches
42 Lo shu, an ancient Chinese figure
42 Magic squares: their history and mathematical features
44 More intricate magic squares
47 Diabolic squares
48 Magic stars
51 More about squares
51 An extraordinary surface
52 The bridges of Kdnigsberg
55 Elementary theory of graphs
57 Save the goat and the cabbage
58 The jealous husbands
61 Interchanging knights
62 A wide range of applications
63 Topology, or the geometry of distortion
70 Topological labyrinths
73 The Mobius ring
76 Games with topological knots
77 The four-colour theorem
84 Rubik's cube
91 Paradoxes and antinomies
91 The role of paradoxes in the development of mathematical thought
94 Geometrical representation of numbers
94 A tragic Pythagorean paradox: the odd equals the even
96 Unthinkable numbers
97 Zeno of Elea
98 Zeno's paradoxes
100 Theoretical significance and solution of Zeno's paradoxes
101 The part equals the whole
102 Sets, an antinomic concept
103 A postman and barber in trouble
104 Russell's paradox
105 A great game: mathematical logic
105 A special chessboard
105 What is a logical argument?
106 Logic and ordinary language
107 An ingenious idea of Leibniz
108 Logic: the science of correct reasoning
112 Logical variables
113 George Boole and the origins of propositional calculus
113 The logical calculus
114 Negation
115 Explanation of symbols
115 Conjunction and the empty set
116 The empty set
117 Disjunction
118 Implication
119 Who has drunk the brandy?
120 The multiplication tables of propositional calculus: truth-tables
125 Another solution to the problem of the brandy drinkers
126 Who is the liar?
129 How to argue by diagram
135 A practical application: logic circuits
143 Games with probability
143 The reality of chance and uncertainty
144 Cards, dice, games of chance and bets: historical origins of the calculus of probability
144 Chance phenomena
145 A clarification
146 Sample space
148 The measure of probability
148 Horse races
149 The concept of function
149 The algebra of events and probability games
150 The complementary event and its probability measure
150 The probability of the union of two events
151 The probability of the intersection of two events
152 The probability of a choice
153 Drawing a card from a pack
154 Joint throw of coin and die
154 Dependent events
156 Independent events
159 What is the probability that George and Bob speak the truth?
160 Probability and empirical science
160 Probability and statistics
160 Sample and population
161 Guess the vintage
161 Conclusion
163 Appendix: games with logic and probability
163 Note
164 Games with logic
167 Games with probability
177 List of main symbols used
179 Bibliography
181 Index

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