The Surprise Attack in Mathematical Problems

Louis A. Graham

• Publisher: Dover Publications
• Year: 2017
• eBook ISBN: 9780486820767
• Topic: Mathematics
• Subtopic: Games in Mathematics
• Index: Mathematics

For decades, professionals in applied mathematics and mathematical puzzle fans from all over the world supplied provocative problems to the puzzle columns of the Graham Dial. Upon the appearance of an interesting problem, readers wrote in to the Dial suggesting new approaches to the solution, some greatly simplifying the problem and others broadening its scope. This collection presents 52 of the finest problems, all featuring the "surprise attack" and abounding in imaginative and interesting solutions.
The problems involve measurement of geometrical spaces, probabilities, distances, number systems other than the decimal, interesting number relations, relative motion, and the discovery of the simplest solution through purely logical means. Solutions involve such techniques as arithmetic, algebra and geometry, number theory, statistics, networks, and inversion. Several approaches to the solution accompany each problem, and even the best of these represent not the ideal solution but only the most satisfying — so far.

Table of contents

• Cover
• Title Page
• Copyright Page
• Foreword
• Contents
• 1. Graphic Reciprocals
• 2. Real Estate by Intersections
• 3. Making Change
• 4. Disk Distraction
• 5. The Stamp Dispenser
• 6. Searchlight on Grossed Ladders
• 7. Careless Composition
• 8. Tic-Tac-Toe for Gamblers
• 9. Mathman with a Sense of Humor
• 10. Four Four Finale
• 11. Codes and Computers
• 12. Three Given Altitudes
• 13. Simplification by Projection
• 14. Unequal Integers
• 15. Sport Scores
• 16. Measure of Ribbons
• 17. Clock Watching
• 18. Catch and Carries
• 19. Silver Dollar Saver
• 20. Pell by Succession
• 21. Smallest Triangle
• 22. The Todd County Ranch
• 23. New Route to Roots
• 24. Lost Paddle and Passing Trains
• 25. Quickies
• 26. Merry Xmas to All
• 27. Little Euclid’s Age
• 28. Right Angle Check
• 29. Tale of a Tile Setter
• 30. Nearest Trisection
• 31. The Will and the Way
• 32. One-Step Double
• 33. Watch Wound Wrong
• 34. The Unknown Center
• 35. The Isosceles Triangle
• 36. Weather in Azuciana
• 37. Bids and Scores in Duplicate Bridge
• 38. The Ranchers’ Split
• 39. Philosophy and Probability
• 40. The Blushing Beauties
• 41. The Car Behind
• 42. Right Triangle Construction
• 43. To Win at Las Vegas
• 44. Sums and Factors
• 45. Base and Bisector
• 46. Who Killed Whom ?
• 47. Again—The Golden Ratio
• 48. The Fourth Generation
• 49. Product with Reverse
• 50. The Powerless Binary
• 51. Doubles on Reverse
• 52. Three Parallels