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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'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 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.
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'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 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.
- GenresNonfictionPuzzlesScience
232 pages, Paperback
First published December 2, 2014
2 people are currently reading
2246 people want to read
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Displaying 1 - 3 of 3 reviews
July 7, 2023
This book is an amazing compilation of mathematical riddles. As someone with a solid background in mathematics, I over-confidently thought I’d be able to breeze through this book, and very quickly realized that this is not your average riddle book. Getting to the solutions in these problems takes some time, which makes the satisfaction of your “eureka” moment so much more rewarding. If you miss college mathematics classes (I do), enjoy logicking through quantitative problems, or just love an analytical challenge, I think this is a great book for you!
April 5, 2023
This is a bit of an oddity that is likely to prove Marmite-like in attracting a mix of enthusiasm and dislike - so three stars is something of an average outcome. The authors describe it as 'a compendium of difficult mathematical riddles'. I don't think this is strictly accurate: these aren't riddles in any conventional sense, they are word-based mathematical problems or puzzles, but lack the wordplay that is essential to a riddle.
Which side of the divide you come down on is likely to depend on two factors. Whether you like indulging in mathematical problems, and whether you only like mathematical problems where an intuitive grasp is enough, or whether you enjoy ploughing through mathematical workings to get to the solution. I suspect my use of the word 'ploughing' there highlights that, while I personally do like them, I haven't the patience for problems that take a lot of working through.
For those of us with limited patience, there is a hints section that gives something of a pointer to the way of approaching the problem, before a detailed solutions section (the longest part of the book). It's probably best to give an example. The first 'riddle' says that a blacksmith has five chains, each with three links. He wants to make a chain 15 links long. Given he can open and close links, what is the minimum number he needs to open. The hint tells us that four links is obvious, but is it optimal? And the solution gives the actual answer.
Here the answer is practically one line: this is the kind of intuitive puzzle I find appealing. But with a fair number there was some mathematical working required. The subtitle mentions these are 'classic' riddles - and almost every popular mathematical problem I've come across is in there, from Monty Hall to the seven bridges of Koenigsberg, via plenty of statistical and speed of travel problems, both familiar and novel.
In practice, I did enjoy it rather more than I thought I would, though for me it would have worked better if the solutions had come straight after the relevant problems - I spent most of my time reading a problem, failing to solve it then flipping to the back to read the solution.
Not at all a bad book (though I wish the cover had looked a little less self-published) - but one with a very specific readership. You'll know if it's for you - and if it is, you should get a copy.
Which side of the divide you come down on is likely to depend on two factors. Whether you like indulging in mathematical problems, and whether you only like mathematical problems where an intuitive grasp is enough, or whether you enjoy ploughing through mathematical workings to get to the solution. I suspect my use of the word 'ploughing' there highlights that, while I personally do like them, I haven't the patience for problems that take a lot of working through.
For those of us with limited patience, there is a hints section that gives something of a pointer to the way of approaching the problem, before a detailed solutions section (the longest part of the book). It's probably best to give an example. The first 'riddle' says that a blacksmith has five chains, each with three links. He wants to make a chain 15 links long. Given he can open and close links, what is the minimum number he needs to open. The hint tells us that four links is obvious, but is it optimal? And the solution gives the actual answer.
Here the answer is practically one line: this is the kind of intuitive puzzle I find appealing. But with a fair number there was some mathematical working required. The subtitle mentions these are 'classic' riddles - and almost every popular mathematical problem I've come across is in there, from Monty Hall to the seven bridges of Koenigsberg, via plenty of statistical and speed of travel problems, both familiar and novel.
In practice, I did enjoy it rather more than I thought I would, though for me it would have worked better if the solutions had come straight after the relevant problems - I spent most of my time reading a problem, failing to solve it then flipping to the back to read the solution.
Not at all a bad book (though I wish the cover had looked a little less self-published) - but one with a very specific readership. You'll know if it's for you - and if it is, you should get a copy.
December 23, 2025
Una colección de acertijos bastante complejos, algunos de los cuales necesitan demostraciones matemáticas complicadas.
Displaying 1 - 3 of 3 reviews