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.

《蛋糕的價值》是克萊門特和吉廖姆·德蘭德斯兄弟精心設計的數學謎題集，適合坐在沙發上的數學愛好者和經驗豐富的數學家，無論是高中生還是更高年級的學生都能從中獲得樂趣。這本書以難度分類，並附有獨特的手繪插圖，呈現了一系列豐富且易於理解的數學謎題。這些挑戰在範圍和精確度上都非常出色，沒有任何“詭計”，只有用來測試你技能的優質數學問題。

任何學生都會對重新呈現的經典難題，如辛普森悖論、希爾伯特的無窮旅館、蒙蒂霍爾悖論和孔尼斯堡的七座橋感到興奮，而經驗豐富的解題者也會喜歡使用選擇公理和康威士兵問題的具有挑戰性的原創謎題。德蘭德斯兄弟清晰而優雅的解答提供了新的見解，將每個問題中應用的技能與更廣泛的理論發現無縫地聯繫起來。此外，正如菲爾茲獎得主塞德里克·維拉尼在序言中寫道，這些謎題不僅僅是練習題。它們捕捉到了“一定程度的端莊和神秘感”，要解開它們需要想像力和毅力。

為了幫助你在這個旅程中，作者提供了每個謎題的提示、詳細的證明和解答，以及一系列數學複習，重新學習用於解答這些問題的重要概念。《蛋糕的價值》既有趣又嚴謹，一定能吸引數學愛好者和各個級別的學生。

Clément Deslandes is a current PhD candidate in mathematics at the École Polytechnique.

Guillaume Deslandes teaches undergraduate-level mathematics at College Stanislas in Paris.

Clément Deslandes 是 École Polytechnique 的一位數學博士候選人。Guillaume Deslandes 在巴黎的 College Stanislas 教授本科水平的數學。