Ingeniously designed mathematical riddles to delight armchair—and seasoned—mathematicians, in high school and beyond.
In The Price of Cake, brothers Clément and Guillaume Deslandes have assembled a uniquely rich and accessible collection of mathematical riddles, organized by difficulty and accompanied by unique hand-drawn illustrations. The challenges are exceptional in both their range and their precision. There are no “tricks” here—just good math to test your skills.
While any student will be thrilled to encounter fresh presentations of classic conundrums such as Simpson’s paradox, Hilbert's infinite hotel, Monty Hall’s paradox, and Seven Bridges of Königsberg, seasoned solvers will also appreciate challenging original puzzles using the Axiom of Choice and Conway’s Soldiers problem. The Deslandes’ lucid and elegant solutions offer new insights, as they seamlessly connect the skills applied in each problem to broader theoretical revelations. Moreover, as Fields Medalist Cédric Villani writes in his preface, these riddles are much more than just exercises. They capture “a certain dose of decorum and mystery,” and to decipher them will require both imagination and tenacity.
To aid you on this journey, the authors provide hints to each puzzle, detailed proofs and solutions, and a series of Math Refreshers to revisit important concepts that are used to arrive at those answers. Entertaining and rigorous in equal measure, The Price of Cake is bound to captivate mathematics enthusiasts and students of all levels.
Author(s): Clément Deslandes, Guillaume Deslandes, Lorenzo Croissant (Translator)
Edition: 1
Publisher: The MIT Press
Year: 2023
Language: English
Pages: 232
City: Cambridge, MA
Tags: Mathematical Recreations; Mathematical Riddles; Math Puzzles
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
