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. |
Contents
Foreword | 9 |
Preface | 4 |
Page | 7 |
Exercise on the multiplication table 11 55 | 7 |
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 | 24 |
The tying of boxes 33 133 | 24 |
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 |
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 21 | 99 |
Octahedron 21 | 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 |
ballbearings 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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Common terms and phrases
29 February A₁ abacus Abracadabrus angle appear arbitrary axis B₁ belongs C₂ centre chessboard choose circle circle K colour column consider contradiction convex corner cube d₁ d₂ diagonal diagram diameter digits disk distance divided dodecahedron edges ellipse equal equation faces follows four geodesics given halving the perimeter hedron hexagon hexahedra hexahedron inequality integral numbers intersecting irreducible fraction lattice length Let us denote Let us suppose letters marked fish mathematics natural numbers nodes numbers X1 obtain octahedron parabola parallel pawn pentagon permutation perpendicular place the rooks plane plots polygon polyhedron possible primary division problem prove pupils rectangle rectangular rhombic dodecahedron rhombus rooks rotation satisfying the conditions segment sequence ship shortest giant shown in Fig sides solution speed sphere straight lines halving symbols symmetry tallest midget tangent tetrahedron theorem triangle vertex vertices white squares Wrocław