Mathematical Diamonds

1. The remarkable wine-rack property; 2. The Restless Lion; 3. Apples and sticks; 4. A surprising result of Paul Erdös; 5. Miscellaneous gleanings; 6. An application of Tur´an's theorem; 7. Four problems from Putnam papers; 8. Topics based on problems from Quantum; 9. Two distinguished integers; 10. A property of the binomial coefficients; 11. Nine miscellaneous problems; 12. A problem in coin-tossing; 13. Semi-regular lattice polygons; 14. Six problems from the Canadian Open Mathematics Challenge; 15. Three pretty theorems in geometry; 16. Two gems from Euclidean geometry; 17. The Thue–Morse–Hedlund sequence; 18. Two miscellaneous problems; 19. A surprising property of regular polygons; 20. Three short stories in number theory; 21. Three geometry problems; 22. Three problems from the 1990 Balkan Olympiad; 23. A Japanese 'fan' problem; 24. Slicing a doughnut; 25. A problem from the 1980 Tournament of the Towns.