## One Hundred Problems In Elementary Mathematics (Popular Lectures in Mathematics Vol. 7)- Steinhaus

In this post, we will see the book One Hundred Problems In Elementary Mathematics by Hugo Steinhaus. his book is volume 7 of Popular Lectures in Mathematics series.

This booklet is an answer to a challenge: a few years after the war the inadequacy of mathematical education in our high schools became evident to the staffs of universities and technological institutes. Some responsible people felt that a closer collaboration between mathematicians and school teachers could no longer be postponed. A few scientists were among those who did their best to stimulate interest in mathematics by means of elementary problems published in an educational journal. Here the reader will find one hundred elementary problems and their solutions. Some of them are familiar to students in high schools, but it was by no means my intention to provide the teacher with questions he could find in every textbook.

The book was translated from Polish and published in 1964.

You can get the book here.

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# Contents

Foreword
Preface

## Chapter I PROBLEMS ON NUMBERS, EQUATIONS AND INEQUALITIES

Problem Solution

1. Exercise on the multiplication table 11 55
2. An interesting property of numbers 11 55
3. Division by 12 58
4. The divisibility of numbers 12 59
5. A simplified form of Fermat’s theorem 12 60
6. Distribution of numbers 12 61
7. Generalization 13 61
8. Proportions 13 65
9. Irrationality of the root 13 65
10: Inequality 13 65
11. A sequence of numbers 13 67

## Chapter II PROBLEMS ON POINTS, POLYGONS, CIRCLES AND ELLIPSES

12. Points in a plane 14 68
13. Examination of an angle 14 69
14. Area of a triangle 14 69
15. Triple halving of the perimeter of a triangle 15 70
16. Division of a triangle 15 75
17. Triangles 15 77
18. Triangular network 15 77
19. Triangular network 16 78
20. What is left from a rectangle? 16 79
21. Division of a square 16 81
22. Square network 16 83
23. Lattice points 17 84
24. Lattice points inside a circle 17 84
25. 14 = 15 17 85
26. Polygon 17 85
27. Points and a circle 18 86
28. Geometrical problem 18 87

## Chapter III PROBLEMS ON SPACE, POLYHEDRA AND SPHERES

29. Division of space 19 89
30. Two projections 19 89
31. Cube 19 90
32. Geodesics 20 92
33. Motion of a particle 20 95
34. Diagrams of the cube 20 96
35. Cubes 21 96
36. Hexahedron 21 98
34. Tetrahedra 21 98
38. Tetrahedron with congruent faces 21 99
39. Octahedron 21 101
40. Distance on a surface 21 103
4l. The wandering of a fly 22 104
42. Regular dodecahedron 22 105
43. Polyhedron 22 108
44. Non-convex polyhedron 23 109
45. Problem from Wonderland 23 110
46. Three spheres and a line 24 113
47. A property of the sphere 24 113

## Chapter IV PRACTICAL AND NON-PRACTICAL PROBLEMS

48. Puzzle 25 115
49. Picnic ham 25 115
50. Quartering of a pie 26 116
51. Another pie 26 117
52. Weighings 26 118
55. Calibration of rollers 27 121
56. 120 ball-bearings 28 121
57. Ribbon on the roll 28 122
58. Watch with both hands identical 28 123
59. Problems of giants and midgets 29 125
60. Acks and backs 29 127
61. Statistics 30 127
62. Blood groups 31 128
63. Blood groups again 32 129
64. Excess of labour 32 130
65. Diagonal of a wooden block 32 133
66. The tying of boxes 33 133
67. A primitive device 33 134
68. The minimal length 33 136
69. Division of plots 34 136
70. A practical problem 34 143
71. Neighbouring towns 35 144
72. Railway lines (I) 35 145
73. Railway lines (II) 35 146
74. Test Flight 35 149
75. Sun and Moon 36 150
76. Cosmography 36 150

## Chapter V PROBLEMS ON CHESS, VOLLEYBALL AND PURSUIT

77. Chessboard 37 153
78. Chessboard revisited 37 153
79. Rooks on the chessboard 37 157
80. Elliptical billiards 38 161
81. A sports problem (I) 38 162
82. A sports problem (II) 38 162
83. Theory of sport eliminations 38 163
84. Volleyball league 39 164
85. Tournaments 39 165
86. Bicyclist and walkers 40 165
87. Four dogs 40 166
88. Chase (I) 41 166
89. Chase (II) 41 167
90. Incomplete data 41 168
91. Motorboat (I) 41 168
92. Motorboat (II) 42 169

93. The strange number 43 171
94. The tailor’s tape 43 171
95. Word quiz 43 171
96. Student debts 44 172
97. A strange social set 44 172
98. ABACUS 44 173
99. Washing the streets 45 174
100. French cities 45 174

## Chapter VII PROBLEMS WITHOUT SOLUTION

Plus and minus 47
Triangle in a triangle 48
Parts of a square 48
Division of a circle 49
Unlimited chessboard 49
The abacus again 49
Tins in a drawer 50
Bacilli 50
The circus is coming 50
Three Cowboys 51
Investigation 51
Arrows on a dodecahedron 52

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### 2 Responses to One Hundred Problems In Elementary Mathematics (Popular Lectures in Mathematics Vol. 7)- Steinhaus

1. Awarikabey Emmanuel says:

Dear Mir Books,I am grateful for the valuable books that you send to me via email. I want to check with you, do you have a pdf version of the book title Examples and problems to the course of unit operations of chemical engineering by K. F. Pavlov P. G. Romankov A. A. Noskov Kindly send me a copy of this book if you have or link me up to where I can get this book.
Kind regards,
Emmanuel Awarikabey Laboratory Manager ( Assistant Research Fellow)College of EngineeringDepartment of Chemical EngineeringKNUSTTel.: (+233) 20 829 7829        (+233) 24 079 9846Email: eawarikabey.coe@knust.gh.com

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• The Mitr says:

there is a Moldovian version available if that helps

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