This is a Dover reprint of a book first published in 1992 as The Penguin Book of Curious and Interesting Puzzles, and it's very welcome indeed. The book's title certainly ups the ante: are the puzzles really "curious and interesting"? For the most part, yes they are, and the book's historical arrangement makes them even more so.
Mathematical puzzles have been around almost from the beginning. In fact, Wells opens his book with a selection of problems extracted (sometimes with some updating, and often complemented by modern analogues) from ancient sources: the Rhind papyrus, Babylonian tablets, the Greek anthology, Al-Khwarizmi, the Bhakshali manuscript, the Chinese Nine Chapters, Alcuin's Propositions to Sharpen Up the Young, and others. Wells is careful to indicate that he is not really attempting a history of recreational mathematics here, but his arrangement nevertheless raises several interesting historical points. It is remarkable to realize how old some of these puzzles are… and then to realize that they are still interesting, and that some of them are still quite challenging.
In all, Wells' collection has 568 puzzles, and of course the solutions are all there in the back of the book (with, I am joyful to report, bibliographic references). There is a decent index. I was a little upset at the lack of a useful table of contents. If one wants to find the Chinese puzzles, for example, the only way is to leaf through the early portion of the book. The headers indicating a new section are set within the text, so one doesn't even get the signal of a new page. Nevertheless, there is a lot here to be grateful for. It is a very nice, and very useful, collection.
I have been told by many students who have interviewed for consulting jobs that these puzzles (number 439, for example) are showing up in these interviews as tests of mental agility. As a result, books such as this have acquired a surprising new relevance. A few weeks working through this book may be one of the best ways to prepare for such job interviews.
So: this is a very good book, containing lots of good mathematical puzzles and arranged in a particularly interesting way. Students interested in consulting jobs may find it useful as preparation for their job interviews, and anyone who enjoys puzzles will have a lot of fun with it. I am left with only one unsolved puzzle: Book of Curious & Interesting Puzzles is certainly a curious and puzzling title. I can certainly understand deleting the word "Penguin" from the original title, but what happened to the "The"?
Fernando Q. Gouvêa is professor of mathematics at Colby College in Waterville, ME.