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.

# About the book

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.

Credits to original uploader.

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

## Chapter VI MATHEMATICAL ADVENTURES OF DR. ABRACADABRUS

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

Radii in space 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

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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there is a Moldovian version available if that helps

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