The Price of Cake : And 99 Other Classic Mathematical Riddles

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. 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 Ingeniously designed mathematical riddles to delight armchair--and seasoned--mathematicians, in high school and beyond. In The Price of Cake , brothers Clment 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 Knigsberg, seasoned solvers will also appreciate challenging original puzzles using the Axiom of Choice and Conway's Soldiers problem. The Deslandes's 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 Cdric 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. 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. "A novel collection of 100 entertaining math puzzles, many of them original, with hints, copious illustrations, varying degrees of difficulty, and connections to formal math concepts"-- Provided by publisher