The Price of Cake: Clément and Guillaume Deslandes ***

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.

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Review by Brian Clegg - See all Brian's online articles or subscribe to a weekly email free here

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