Ask almost any mathematician who grew up during the 1960s or 1970s, and they'll tell you about the enormous influence Martin Gardner's Mathematical Games column had on them. Every month, Scientific American brought another of Gardner's columns, and we learned about some new bit of entertaining mathematics and had fun trying to solve the puzzles and problems.
For completists, the MAA recently published a CD-ROM containing every single one of Gardner's collections of Mathematical Games columns. For the less ambitious, however, there are the two Colossal Books published by Norton. The Colossal Book of Mathematics: Classic Puzzles, Paradoxes, and Problems, published in 2001, presented a selection from Gardner's columns. The book under review, The Colossal Book of Short Puzzles and Problems, collects a large number of the puzzles and problems that appeared in those columns, plus a few more recent additions. Every so often, Gardner would do a column which was simply a collection of short problems, and these seem to be the source of most of the material collected here.
I often shock my calculus students by telling them of the long afternoon I once spent, in my teens, attempting to solve one of Martin Gardner's problems. The problem boiled down to computing partial sums of the harmonic series, and the solution depended on knowing that the series diverges. This was my first exposure to a divergent series, and it was so memorable that I have never forgotten it. That problem is in here, on page 429. That's enough for me. Even though I have the CD-ROM (and can't imagine anyone not wanting one), there's space in my shelves for this book too.
Fernando Q. Gouvêa is Professor of Mathematics at Colby College and the co-author, with William P. Berlinghoff, of Math through the Ages. He somehow finds time to also be the editor of MAA Reviews.