## One Hundred Problems in Elementary MathematicsA 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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