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. 

Clément Deslandes is a current PhD candidate in mathematics at the École Polytechnique.
 
Guillaume Deslandes teaches undergraduate-level mathematics at College Stanislas in Paris.

Foreword ix
Preface xiii
I Statements 1
Level 1 3
Level 2 19
Level 3 43
II Hints 69
III Solutions 83
IV Reminders 175
1 The Pigeonhole Principle 177
2 Binomial Coefficients 181
3 Equivalence Relations 185
4 Bijections 189
5 Induction 197
6 Congruence 201
7 Bases of Number Systems 205
8 Some Probabilities 207
Bibliography 211
Index 213