{"product_id":"the-price-of-cake-isbn-9780262545242","title":"The Price of Cake","description":"\u003cb\u003eIngeniously designed mathematical riddles to delight armchair—and seasoned—mathematicians, in high school and beyond.\u003c\/b\u003e\u003cbr\u003e\u003cbr\u003eIn \u003ci\u003eThe Price of Cake\u003c\/i\u003e, 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.\u003cbr\u003e \u003cbr\u003eWhile 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.\u003cbr\u003e \u003cbr\u003eTo 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, \u003ci\u003eThe Price of Cake\u003c\/i\u003e is bound to captivate mathematics enthusiasts and students of all levels. Foreword ix\u003cbr\u003ePreface xiii\u003cbr\u003eI Statements 1\u003cbr\u003eLevel 1 3\u003cbr\u003eLevel 2 19\u003cbr\u003eLevel 3 43\u003cbr\u003eII Hints 69\u003cbr\u003eIII Solutions 83\u003cbr\u003eIV Reminders 175\u003cbr\u003e1 The Pigeonhole Principle 177\u003cbr\u003e2 Binomial Coefficients 181\u003cbr\u003e3 Equivalence Relations 185\u003cbr\u003e4 Bijections 189\u003cbr\u003e5 Induction 197\u003cbr\u003e6 Congruence 201\u003cbr\u003e7 Bases of Number Systems 205\u003cbr\u003e8 Some Probabilities 207\u003cbr\u003eBibliography 211\u003cbr\u003eIndex 213\u003cb\u003eClément Deslandes\u003c\/b\u003e is a current PhD candidate in mathematics at the École Polytechnique in France.\u003cbr\u003e\u003cbr\u003e\u003cb\u003eGuillaume Deslandes\u003c\/b\u003e teaches undergraduate-level mathematics at Lycée Stanislas in Paris.","brand":"The MIT Press","offers":[{"title":"Default Title","offer_id":46304436551909,"sku":"NP9780262545242","price":26.95,"currency_code":"USD","in_stock":false}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/1842\/7735\/files\/9780262545242.jpg?v=1767741060","url":"https:\/\/k12savings.com\/products\/the-price-of-cake-isbn-9780262545242","provider":"K12savings","version":"1.0","type":"link"}