One Hundred Problems in Elementary Mathematics

Front Cover
Courier Corporation, Jan 1, 1979 - Science - 174 pages
A stimulating collection of one hundred problems, complete with instructive solutions, on numbers, equations, polygons, polyhedra and many other topics. Extremely challenging for anyone with a fair knowledge of mathematics up to calculus. Includes an additional 13 problems without solutions.
 

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Contents

Foreword
11
Preface
11
Page
11
Exercise on the multiplication table 11 55
11
Division by 11 12 58
12
Generalization 13 61
13
Chapter II
14
Triple halving of the perimeter of a triangle 15 70
15
Polyhedron 22
108
Nonconvex polyhedron 23
109
Problem from Wonderland 23
110
Three spheres and a line 24
113
Chapter IV
115
Quartering of a pie 26
116
Another pie 26
117
Weighings 26
119

Chapter III
19
Diagonal of a wooden block 32 133
32
The tying of boxes 33 133
33
Division of plots 34 136
34
Neighbouring towns 35 144
35
Division of a triangle 15
75
Triangles 15
77
Triangular network II 16
78
What is left from a rectangle ? 16
79
Division of a square 16
81
Square network 16
83
Lattice points 17
84
15 17 85 26 Polygon 17
85
Points and a circle 18
86
Geometrical problem 18
87
Cube 19
90
Geodesics 20
91
Motion of a particle 20
92
Diagrams of the cube 20
95
Cubes 20
96
Tetrahedra 21
98
Tetrahedron with congruent faces 2199
102
Distance on a surface 21
103
The wandering of a fly 22
104
Regular dodecahedron 22
105
How many fish are there in the pond? 27
121
ball bearings 28
122
Watch with both hands identical 29
123
Problems of giants and midgets 29
125
Acks and backs 29
127
Blood groups 31
128
Blood groups again 32
129
Excess of labour 32
130
Sun and Moon 36
150
Chapter V
153
Rooks on the chessboard 37
157
Elliptical billiards 38
161
A sports problem 1 38
162
Theory of sport eliminations 38
163
Volleyball league 39
164
Tournaments 39
165
Four dogs 40
166
Chase II 41
167
Incomplete data 41
168
Motorboat II 42
169
Chapter VI
171
Student debts 44
172
Abacus 44
173
Washing the streets 45
174
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About the author (1979)

Hugo Steinhaus (1887-1972) was among the world's leading mathematicians. Trained in mathematics at Göttingen University, where he received his doctorate, Dr. Steinhaus wrote over 150 papers on pure and applied mathematics as well as several books. The Russian edition of this volume sold over 100,000 copies. His other Dover book is Mathematical Snapshots.

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