Mathematical diamonds

Title page......Page 1
Preface......Page 5
Section 1. The Remarkable Wine-Rack Property......Page 9
Section 2. The Restless Lion......Page 13
Section 3. Apples and Sticks......Page 17
Section 4. A Surpising Result of Paul Erdös......Page 21
Section 5. Miscellaneous Gleanings......Page 27
Section 6. An Application of Turan's Theorem......Page 43
Section 7. Four Problems from Putnam Papers......Page 51
Section 8. Topics Based on Problems from Quantum......Page 57
Section 9. Two Distinguished Integers......Page 87
Section 10. A Property of the Binomial Coefficients......Page 91
Section 11. Nine Miscellaneous Problems......Page 95
Section 12. A Problem in Coin-Tossing......Page 111
Section 13. Semi-regular Lattice Polygons......Page 117
Section 14. Six Problems from the Canadian Open Mathematics Challenge......Page 125
Section 15. Three Pretty Theorems in Geometry......Page 133
Section 16. Two Gems from Euclidean Geometry......Page 143
Section 17. The Thue-Morse-Hedlund Sequence......Page 151
Section 18. Two Miscellaneous Problems......Page 159
Section 19. A Surprising Property of Regular Polygons......Page 165
Section 20. Three Short Stories in Number Theory......Page 171
Section 21. Three Geometry Problems......Page 177
Section 22. Three Problems From The 1990 Balkan Olympiad......Page 183
Section 23. A Japanese "Fan" Problem......Page 189
Section 24. Slicing a Doughnut......Page 195
Section 25. A Problem from the 1980 Tournament of the Towns......Page 203
More Challenges......Page 211
Solutions To The Challenges......Page 217
Indices......Page 245