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What is the Name of This Book? - Raymond Smullyan ***

This classic recreational mathematics title, based on logic problems (thanks to Tim Harford for the recommendation) dates back to 1978, though it feels as if it might have been written forty years earlier from the type of humour it features, a feeling enhanced by the publisher's decision to reprint it by scanning an old edition, rather than resetting it.

There is some excellent material in here, some familiar, others still with a novel edge today. There are some basic challenges - for example we're looking at a picture and told 'Brothers and sisters have I none, but this man's son is my father's son' and asked whose picture it is, plus some catch-you-out puzzles such as asking in which country you'd bury the survivors of a plane that crashes right on the border of the US and Canada. But the meat and drink of the book is a whole slew of puzzles where we are required to deduce something from a set of logical statements.

Many of these puzzles are based on variants of a situation where there are two different kinds of people, one type who who always lies and the other type who always tells the truth (sometimes there is a third kind who might do either). These problems come in all sorts of variants featuring knights and knaves, Dracula, zombies and more, but the basic principles are aways the same, though the combinations become more and more convoluted. There are also a very similar feeling set of puzzles where a number of statements are put against each other, such as caskets with labels on that indicate between them where treasure is located. And we also get some consideration of the extremes where logical statements become meaningless, such as 'This statement is false.'

The truth/lie problems take up significantly more than half of the book, and after the first few I did find these too much like work rather than fun and couldn't be bothered to work them out. The fun in mathematical puzzles and diversions comes from novelty - when you are presented with one problem after another that is just a variant on the previous one, it becomes hard to retain much enthusiasm.

There were also some examples of logic problems that suffer very badly from the 'only one solution' fallacy, which can be a failing in mathematicians. One that's in the book involves a person who every day leaves his flat on (say) the 25th floor and every evening comes home but gets out on (say) the 23rd floor. Why? Raymond Smullyan gives us the traditional 'right' answer - but I've used this as an exercise in creativity sessions and had more than 20 right different, equally valid, right answers proposed. This is the difference between problems set in the real world and those in a mathematical world where you can have someone who 'always lies'.

There's also something of an oddity in that Smullyan repeatedly asks us through the book 'What is the name of this book?' I was expecting some kind of clever-clever response like 'What' (because 'What' is the name of this book), although the question mark at the end of the title rather precludes it being a statement. But Smullyan responds 'Well, the name of the book is "What is the Name of This Book?". Since that is what's printed on both the cover and the spine, it's hard to be surprised. I can only guess that, since the illustration has most of the title ripped off, that the original version didn't also have the full title printed on it. Otherwise it's a very limp ending.

Overall, there's some excellent material here, but if you stripped out the dated humour and the repetition of variants on the same problem, what's left is probably not much more than a long magazine article.

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