The Price of Cake: And 99 Other Classic Mathematical Riddles

Contents
Foreword
Preface
I. Statements
	Level 1
		1. A Lazy Blacksmith
		2. Bumper Ants
		3. The Price of Cake
		4. The Ketchup Fry
		5. Going Around in Circles
		6. The Soft-Boiled Egg
		7. A Pill Mix-up
		8. A Hurried Student
		9. Going Upstream
		10. Boys and Girls
		11. Café au Lait
		12. Lait au Café
		13. Guardians of the Gates
		14. A Kangaroo on a Staircase
		15. The Fluttering Fly
		16. An Hour Early
		17. How to Cut Up a Cube
		18. Racing to a Hundred
		19. Fresh Paint!
		20. The Worldly Cocktail Party
		21. Same Time and Place
		22. Taking It a Coin Too Far
		23. The Birthday Paradox
		24. Fifteen Serpents
		25. A Screening Test
		26. Shocking Sports Statistics
	Level 2
		27. Free Throws
		28. The Number Across the Street
		29. The Unstable Painting
		30. The Unfaithful Spouses
		31. A Few Surprising Probabilities
		32. The Monty Hall Problem
		33. Square Jigsaws
		34. The Good, the Bad, and the Ugly
		35. The Gas Shortage
		36. An Impossible Prediction
		37. With Three Weighings
		38. Heads or Tails in the Dark
		39. The Principal and the Hats
		40. The Fort
		41. Exact Opposites
		42. Hilbert’s Hotel
		43. A Chaotic Boarding
		44. Mutineer Pirates
		45. The Monkey Race
		46. Dwarf Thieves
		47. Eight Triangles to a Square
		48. How to Tile One’s Bathroom
		49. One More Coin
		50. A New Variant of Heads or Tails
		51. The Little Brother’s Revenge
		52. Unbreakable Plates
		53. The Cable Around the Earth
		54. The Spaghetti
		55. Swimming Pool Lockers
		56. Met at a Party
		57. The Rats and the Bottles
		58. The Collection of Cards
		59. The Saint Petersburg Paradox
		60. The Chocolate Bar
		61. Tic-Tac-Toe
		62. Ant vs. Car
		63. The Squirrel and the Nuts
	Level 3
		64. The Triangular Cake
		65. A Fair Share
		66. The Lonely Soldier
		67. The Booty of the Thirteen Pirates
		68. Reference Weights
		69. The Elephant and the Bananas
		70. The Very Hungry Termite
		71. The Principal and the Lightbulb
		72. The Principal and the Drawers
		73. The Principal and the Seven Hats
		74. The Principal and the T-Shirts
		75. Die Hard
		76. The Rats and the Bottles (2)
		77. Where Is the Robot?
		78. The Seven Bridges of Königsberg
		79. Linking the Edges
		80. A Magic Trick
		81. How to Tile One’s Bathroom (2)
		82. How to Tile One’s Bathroom (3)
		83. The Mad Postman
		84. Mind the Dog!
		85. The Two Envelopes
		86. The Two Envelopes (2)
		87. The Squirrel and the Nuts (2)
		88. The Monkey with a Typewriter
		89. A Rectangle with Integer Sides
		90. Finding the Right Wire
		91. Making Friends
		92. Red or Black?
		93. Finding the Cable
		94. Lukewarm Earnings
		95. Not Your Usual Game of Chess
		96. The Principal and the Real Hats
		97. The Principal and the Hats (2)
		98. One Last Riddle with the Principal
		99. The Lax Captain
		100. Peg Solitaire
II. Hints
III. Solutions
IV. Reminders
	1. The Pigeonhole Principle
		Statement of the Principle
		Examples of Applications
		Comparison of Outcomes to Hypotheses
		Riddles Using the Pigeonhole Principle
	2. Binomial Coefficients
		Computation of “n choose p”
		Some Useful Properties
		Riddles Using Binomial Coefficients
	3. Equivalence Relations
		Definition of Equivalence Relations
		Examples of Equivalence Relations
		Equivalence Classes and Representatives
		Riddles Using Equivalence Relations
	4. Bijections
		An Introduction to the Concept of Bijection
		Surjectivity, Injectivity
		Examples of Bijections
		Permutations
		Riddles Using Bijections
	5. Induction
		An Introduction to Induction
		Strong Induction
		An Example of Induction
		An Example of Fallacious Induction
		Riddles Using Induction
	6. Congruence
		The Concept of Divisibility
		Definition of Congruence
		Properties of the congruent with Relation
		An Application to Cryptography
		An Application to a Divisibility Problem
		An Applications to Infeasible Computations
		Riddles Using Congruence
	7. Bases of Number Systems
		Base 10
		Base 2
		Numbering in Base 2
		Riddles Using Base 2 Numbering
	8. Some Probabilities
		Independence and Conditional Probabilities
		Bayes’ Rule
		Riddles Using Probability
Bibliography
Index