Bicycle or Unicycle？_A Collection of Intriguing Mathematical Puzzles

Cover
Title page
Copyright
Contents
Preface
Part 1 Problems
	Chapter 1. Can a Bicycle Simulate a Unicycle?
		1. Bicycle or Unicycle?
	Chapter 2. Geometry
		2. Trisecting to Benefit Society
		3. Ten Bottles of Wine
		4. Into the Woods
		5. The Attraction of the Golden Ratio
		6. Reflect on This
		7. Skewed Pizza
		8. Four-Regular Squares
		9. Venn Symmetry
		10. A Crosscut Quadrilateral
		11. The Legacy of H. G. Wells
		12. Tiling Surprise
		13. A Well-Balanced Clock
		14. On the Level
		15. A Polyhedral Puzzle
		16. Wiggle Room
		17. Drink Me
		18. Right-Angled Polygons
		19. A Rolling Parabola
		20. Rocket Science
		21. The Icing on the Cake
		22. More Cake
	Chapter 3. Number Theory
		23. Power Matching
		24. Triplets
		25. The Mysterious Seventeenth Divisor
		26. True or False?
		27. An Exponential Diophantine Problem
		28. A Prime Characterization
		29. Two Sums and Many Differences
		30. Reciprocals to Squares
		31. Nondivisibility by 11
		32. Equally Powerful Splits
		33. Tripling in Two Steps
		34. Root Closure
		35. A Double Power Leads to a Sum of Two Squares
		36. Prime Subsets
		37. The Incredible Shrinking Superpowers
		38. Special Numbers
	Chapter 4. Combinatorics
		39. Power up Your Radio
		40. A Parking Puzzle
		41. A Black and White Issue
		42. A Choice Problem
		43. Water Wave
		44. An Acceptable Committee
		45. A Compatible Committee
		46. Using Blocks and Chains to Unlock a Safe
		47. A Universal Set of Directions
		48. A Competition Problem About a Competition Problem
	Chapter 5. Probability
		49. The Importance of Irrelevant Information
		50. Creeping Ants
		51. Roll the Dice
		52. Conditioned Throws of a Die
		53. Where Are the Rounded Powers of Two?
		54. The Holy Game of Poker
		55. A Shrinking Random Walk
		56. BINGO!
		57. How Much is a Penny Worth?
		58. A Historically Interesting Truth-Teller Problem
		59. Monty Hall Revisited
	Chapter 6. Calculus
		60. Integrating a Base Change
		61. A T-Shirt Gun
		62. Shooting Range
		63. Convergent Rational Enumeration
		64. A Functional Equation
		65. Two Eerie Recursions
		66. Stabilizing a Cylinder
		67. ? Coincidence?
		68. The Chase Is On
	Chapter 7. Algorithms and Strategy
		69. Where’s Bob?
		70. It’s a Horse Race
		71. Your Two Best Shots
		72. Determine the Martian Majority
		73. Majority Rules
		74. Going for Gold
		75. The Mensa Correctional Institute
		76. Matching Hats
		77. One Hat Too Many
		78. The Prisoners Must Agree
		79. How to Use Irrelevant Information
		80. Flipping Pennies
		81. Battleship Destruction
		82. Real Battleship Destruction
		83. A Very Local Maximum
		84. Detecting a Black Hole
		85. Pablito’s Solitaire
		86. Are the Coins Authentic?
		87. Web Site Analysis
		88. Find the Car, and the Car Key
		89. Magic Coins
		90. Russian Cards
		91. The Generous Automated Teller Machine
	Chapter 8. Miscellaneous
		92. A Self-Descriptive Crossword
		93. Serious Implications
		94. Hermione Granger and the Deadly Bottles
		95. Forbidden Polynomials
		96. A Polynomial Scandal
		97. Pascal’s Determinant
		98. Pains of Imperfect Glass
		99. On the Highway
		100. A Running Mystery
		101. The Star of This Problem is Addition
		102. Don’t Get Your Wires Crossed
		103. Weight Loss Through Juggling
		104. Cantor Set Arithmetic
		105. The Miracle of the Colliding Blocks
Part 2 Solutions
	Chapter 1. Can a Bicycle Simulate a Unicycle?
		1. Bicycle or Unicycle?
	Chapter 2. Geometry
		2. Trisecting to Benefit Society
		3. Ten Bottles of Wine
		4. Into the Woods
		5. The Attraction of the Golden Ratio
		6. Reflect on This
		7. Skewed Pizza
		8. Four-Regular Squares
		9. Venn Symmetry
		10. A Crosscut Quadrilateral
		11. The Legacy of H. G. Wells
		12. Tiling Surprise
		13. A Well-Balanced Clock
		14. On the Level
		15. A Polyhedral Puzzle
		16. Wiggle Room
		17. Drink Me
		18. Right-Angled Polygons
		19. A Rolling Parabola
		20. Rocket Science
		21. The Icing on the Cake
		22. More Cake
	Chapter 3. Number Theory
		23. Power Matching
		24. Triplets
		25. The Mysterious Seventeenth Divisor
		26. True or False?
		27. An Exponential Diophantine Problem
		28. A Prime Characterization
		29. Two Sums and Many Differences
		30. Reciprocals to Squares
		31. Nondivisibility by 11
		32. Equally Powerful Splits
		33. Tripling in Two Steps
		34. Root Closure
		35. A Double Power Leads to a Sum of Two Squares
		36. Prime Subsets
		37. The Incredible Shrinking Superpowers
		38. Special Numbers
	Chapter 4. Combinatorics
		39. Power up Your Radio
		40. A Parking Puzzle
		41. A Black and White Issue
		42. A Choice Problem
		43. Water Wave
		44. An Acceptable Committee
		45. A Compatible Committee
		46. Using Blocks and Chains to Unlock a Safe
		47. A Universal Set of Directions
		48. A Competition Problem About a Competition Problem
	Chapter 5. Probability
		49. The Importance of Irrelevant Information
		50. Creeping Ants
		51. Roll the Dice
		52. Conditioned Throws of a Die
		53. Where Are the Rounded Powers of Two?
		54. The Holy Game of Poker
		55. A Shrinking Random Walk
		56. BINGO!
		57. How Much is a Penny Worth?
		58. A Historically Interesting Truth-Teller Problem
		59. Monty Hall Revisited
	Chapter 6. Calculus
		60. Integrating a Base Change
		61. A T-Shirt Gun
		62. Shooting Range
		63. Convergent Rational Enumeration
		64. A Functional Equation
		65. Two Eerie Recursions
		66. Stabilizing a Cylinder
		67. ? Coincidence?
		68. The Chase Is On
	Chapter 7. Algorithms and Strategy
		69. Where’s Bob?
		70. It’s a Horse Race
		71. Your Two Best Shots
		72. Determine the Martian Majority
		73. Majority Rules
		74. Going for Gold
		75. The Mensa Correctional Institute
		76. Matching Hats
		77. One Hat Too Many
		78. The Prisoners Must Agree
		79. How to Use Irrelevant Information
		80. Flipping Pennies
		81. Battleship Destruction
		82. Real Battleship Destruction
		83. A Very Local Maximum
		84. Detecting a Black Hole
		85. Pablito’s Solitaire
		86. Are the Coins Authentic?
		87. Web Site Analysis
		88. Find the Car, and the Car Key
		89. Magic Coins
		90. Russian Cards
		91. The Generous Automated Teller Machine
	Chapter 8. Miscellaneous
		92. A Self-Descriptive Crossword
		93. Serious Implications
		94. Hermione Granger and the Deadly Bottles
		95. Forbidden Polynomials
		96. A Polynomial Scandal
		97. Pascal’s Determinant
		98. Pains of Imperfect Glass
		99. On the Highway
		100. A Running Mystery
		101. The Star of This Problem is Addition
		102. Don’t Get Your Wires Crossed
		103. Weight Loss Through Juggling
		104. Cantor Set Arithmetic
		105. The Miracle of the Colliding Blocks
Bibliography
Index
	Back Cover