Famous puzzles of great mathematicians

Cover page......Page 1
Title page......Page 2
Contents......Page 6
Preface......Page 14
Art and photo credits......Page 18
1.  RECREATIONAL MATHEMATICS......Page 20
2.  ARITHMETICS......Page 28
Diophantus\' age (Diopbantus)......Page 29
Number of arrows (Mahavira)......Page 30
How many rabbits? (Fibonacci, p. 11)......Page 31
Square numbers problem (Fibonacci)......Page 34
Money in a pile (Fibonacci)......Page 35
Triangle with integral sides (Bachet)......Page 36
Weights problem ( Fibonacci, Tartaglia, Bachet)......Page 39
Division of 17 horses (Tartaglia, p. 23)......Page 43
Coins in hands (Recorde)......Page 44
Sides of two cubes (Viète, p. 25)......Page 45
Animals on a field (Newton)......Page 46
Gathering an army (Alcuin of York)......Page 48
Answers to Problems......Page 49
3.  NUMBER THEORY......Page 56
Cattle problem (Archimedes, p. 38)......Page 60
Dividing the square (Diophantus)......Page 63
Amicable numbers (ibn Qorra)......Page 64
How many soldiers? (Bhaskara)......Page 67
Horses and bulls - a Diophantine equation (Euler)......Page 69
The sailors, the coconuts, and the monkey (P. Dirac)......Page 71
Unknown address (Ramanujan)......Page 76
Stamp combinations (Frobenius, Sylvester, p. 60)......Page 80
Answers to Problems......Page 83
4.  GEOMETRY......Page 86
Arbelos problem (Archimedes)......Page 87
Minimal distance (Heron)......Page 92
The same distance of traversed paths (Brahmagupta)......Page 96
Height of a suspended string (Mahavira)......Page 97
The diameter of the material sphere (ibn Qorra)......Page 99
Dissection of three squares (Abu\'l-Wafa)......Page 100
Billiard problem (Alhazen)......Page 102
Distance of the optimal viewpoint (Regiomontanus)......Page 105
The minimal sum of distances in a triangle (Steiner, Fernnat, Torricelli, Cavalieri)......Page 110
Volumes of cylinders and spheres (Kepler, p. 93)......Page 113
Dido\'s problem (Steiner, p. 95)......Page 115
Division of space by planes (Steiner)......Page 117
Road system in a square (Steiner)......Page 120
Kissing circles (Soddy, Descartes, Kowa)......Page 123
The shortest bisecting arc of area (Polya)......Page 129
Answers to Problems......Page 131
5.  TILING AND PACKING......Page 138
Mosaics (Kepler)......Page 140
Escher\'s mosaics......Page 143
Nonperiodic tiling (Penrose, Conway)......Page 145
Maximum area by pentaminoes (Knuth)......Page 148
Kissing spheres (D. Gregory, Newton)......Page 153
The densest sphere packing (Kepler, Gauss)......Page 156
Cube-packing puzzles (Conway)......Page 161
Answers to Problems......Page 163
6.  PHYSICS......Page 170
The gold crown of King Hiero (Archimedes)......Page 171
The length of traveled trip (Oresme)......Page 172
Meeting of ships (Lacas, p. 155)......Page 175
A girl and a bird (Von Neumann. p. 157)......Page 177
The lion and the man (Littlewood, Bcsicovitch, R. Rado)......Page 180
Answers to Problems......Page 185
7.  COMBINATORICS......Page 190
Combination with flavors (Mahavira)......Page 191
Married couples cross the river (Bachet)......Page 192
Josephus problem (Bachet and others)......Page 195
Rings puzzle (Cardano, p. 180)......Page 200
The problem of the misaddressed letters (N. (11) Bernoulli, Euler)......Page 203
Eulerian squares (Euler)......Page 205
Kirkman\'s schoolgirls problem (Kirkman, Steiner. Sylvester, Cayley)......Page 208
Counting problem (Cayley)......Page 212
Races with ties......Page 213
The tower of Hanoi (Lucas)......Page 215
Interchanging the checkers (I) (Lucas)......Page 218
Interchanging the checkers (II) (Lucas)......Page 219
Shunting problem (Lucas)......Page 119
Problem of married couples (problème ties ménages) (Lucas)......Page 220
The tree planting problem (Sylvester)......Page 221
Answers to Problems......Page 225
8.  PROBABILITY......Page 228
The problem of the points (Fermat, Pascal. p. 211)......Page 231
Gambling game with dice (Huygens)......Page 234
Gambler\'s ruin problem (Pascal, Fermat, Huygens)......Page 236
The Petersburg paradox (N. (III) Bernoulli, D. Bernoulli, Cramer......Page 239
The probability problem with the misaddressed letters (N. (II) Bernoulli, Euler)......Page 241
Matchbox problem (Banach)......Page 243
Answers to Problems......Page 244
9.  GRAPHS......Page 248
The problem of Köningsberg\'s bridges (Euler)......Page 249
Hamilton\'s game on a dodecahedron (Hamilton, p. 233)......Page 253
A man, a wolf, a goat and a cabbage (Alcuin of York)......Page 259
A stout family crosses the river (Alcuin of York)......Page 261
Seven towns and one-way roads (Eadös)......Page 263
Poinsot\'s diagram-tracing puzzle (Poinsot)......Page 264
Milk puzzle (Poisson)......Page 266
Listing\'s diagram-tracing puzzle (Listing)......Page 268
Answers to Problems......Page 269
10.  CHESS......Page 276
Knight\'s re-entrant route (de Moivre, de Montmort, Vandermonde, Euler)......Page 277
Non-attacking rooks (Euler)......Page 284
The eight queens problem (Gauss, p. 268)......Page 288
The longest uncrossed knight\'s tour (Knuth)......Page 292
Guarini\'s knight-switching problem......Page 293
Answers to Problems......Page 295
Problems from Abu\'!-Wafa......Page 302
Amusing problems from Fibonacci......Page 303
Huygens\' probability problems......Page 304
Problems from Euler......Page 305
APPENDIX A: Method of continued fractions for solving Pell\'s equation......Page 308
APPENDIX B: Geometrical inversion......Page 312
APPENDIX C: Some basic facts from graph theory......Page 313
APPENDIX D: Linear difference equations with constant coefficients......Page 315
Biographies - a chronological order......Page 318
Bibliography......Page 330
Name index......Page 338