The Art of Mathematics: Coffee Time in Memphis

Front Cover
Cambridge University Press, Sep 14, 2006 - Mathematics - 359 pages
Can a Christian escape from a lion? How quickly can a rumour spread? Can you fool an airline into accepting oversize baggage? Recreational mathematics is full of frivolous questions in which the mathematician's art can be brought to bear. But play often has a purpose, whether it's bear cubs in mock fights, or war games. In mathematics, it can sharpen skills, or provide amusement, or simply surprise, and collections of problems have been the stock-in-trade of mathematicians for centuries. Two of the twentieth century's greatest players of problem posing and solving, Erdos and Littlewood, are the inspiration for this collection, which is designed to be sipped from, rather than consumed, in one sitting. The questions themselves range in difficulty: the most challenging offer a glimpse of deep results that engage mathematicians today; even the easiest are capable of prompting readers to think about mathematics. All come with solutions, many with hints, and most with illustrations. Whether you are an expert, or a beginner, oran amateur, this book will delight for a lifetime. - Publisher.
 

Contents

The Problems
1
25
5
Contents ix
13
86
20
888
28
The Hints
36
The Solutions
45
Erdős Problems for Epsilons
48
Perfect Trees
218
Circular sequences
220
Infinite Sets with Integral Distances
222
Finite Sets with Integral Distances
223
Thues Theorem
224
the ThueMorse Theorem
226
the CauchyDavenport Theorem
229
the ErdősGinzburgZiv Theorem
232

Points on a Circle
50
Partitions into Closed Sets
52
Triangles and Squares
53
Polygons and Rectangles
55
African Rally
56
Fixing Convex Domains
58
30
59
Nested Subsets
61
Almost Disjoint Subsets
63
Loaded Dice
64
An Unexpected Inequality
65
the ErdősSelfridge Theorem
66
Independent Sets
68
Expansion into Sums 23
69
A Tennis Match
70
Another Erdős Problem for Epsilons
71
Planar Domains of Diameter 1
73
Orienting Graphs
74
A Simple Clock
75
Neighbours in a Matrix
76
Separately Continuous Functions
77
Boundary Cubes
78
Lozenge Tilings
79
31
93
34
103
36
110
40
116
43
124
46
133
49
140
52
147
55
153
57
159
61
165
Zagiers Inequality
169
Squares Touching a Square
170
Infection with Three Neighbours
171
The Spread of Infection on a Torus
173
Dominating Sequences
174
Sums of Reciprocals
175
Absentminded Passengers
176
Airline Luggage
177
the ErdősKoRado Theorem
179
the MYBL Inequality
180
Five Points in Space
183
Triads
184
Colouring Complete Graphs
186
a Theorem of Besicovitch
187
Independent Random Variables
190
Triangles Touching a Triangle
192
Even and Odd Graphs
193
the MoonMoser Theorem
194
Filling a Matrix
197
the ErdősMordell Theorem
199
Perfect Difference Sets
203
Difference Bases
205
the HardyLittlewood Maximal Theorem
208
Random Words
212
Crossing a Chess Board
214
Powers of Paths and Cycles
216
Powers of Oriented Cycles
217
Subwords of Distinct Words
237
Prime Factors of Sums
238
Catalan Numbers
240
Permutations without Long Decreasing Subsequences
242
a Theorem of Justicz Scheinerman and Winkler
244
the BrunnMinkowski Inequality
246
Bollobáss Lemma
248
Saturated Hypergraphs
252
Hardys Inequality
253
Carlemans Inequality
257
Triangulating Squares
259
Strongly Separating Families
262
Strongly Separating Systems of Pairs of Sets
263
The Maximum EdgeBoundary of a Downset
265
Partitioning a Subset of the Cube
267
Frankls Theorem
269
Even Sets with Even Intersections
271
Sets with Even Intersections
273
Even Clubs
275
Covering the Sphere
276
Lovászs Theorem
277
Partitions into Bricks
279
Drawing Dense Graphs
280
Székelys Theorem
282
PointLine Incidences
284
Geometric Graphs without Parallel Edges
285
Shortest Tours
288
Density of Integers
291
Kirchbergers Theorem
293
Chords of Convex Bodies
294
Neighourly Polyhedra
296
Perles Theorem
299
The Rank of a Matrix
301
a Theorem of Frankl and Wilson
303
Families without Orthogonal Vectors
306
the KahnKalai Theorem
308
Periodic Sequences
311
the FineWilf Theorem
313
Wendels Theorem
315
Planar and Spherical Triangles
318
Hadžiivanovs theorem
319
A Probabilistic Inequality
321
Cube Slicing
322
the HobbyRice Theorem
324
Cutting a Necklace
326
the RieszThorin Interpolation Theorem
328
Uniform Covers
332
Projections of Bodies
333
the Box Theorem of Bollobás and Thomason
335
the RayChaudhuri Wilson Inequality
337
the FranklWilson Inequality
340
Maps from Sn
343
Hopfs Theorem
344
Spherical Pairs
345
Realizing Distances
346
A Closed Cover of S˛
348
the Friendship Theorem of Erdős Rényi and Sós
349
Polarities in Projective Planes
352
Steinitzs Theorem
353
The PointLine Game
356
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