Mathematical Puzzles by Martin Gardner

An early collection of brain teasing quickies

Martin Gardner was a popular and prolific nonfiction author of the latter half of the twentieth century. Just as Carl Sagan was the great popularizer of science during that time period, Gardner was the great popularizer of mathematics. For over 25 years, he wrote a column in Scientific American magazine entitled Mathematical Games, in which he presented all sorts of mathematical curiosities and puzzles and educated readers on the mathematical laws and theories behind them. These columns were collected into over a dozen books that enlarged his audience well beyond the subscription list of Scientific American.

Mathematical Puzzles, an early collection of Gardner’s mathematical writings, was published in 1961 and later rereleased by Dover Publications in 1986 as Entertaining Mathematical Puzzles. The puzzles in this volume are not taken from Gardner’s column in Scientific American. Some of them previously appeared in a magazine called Science World, for which Gardner also wrote a column entitled On the Light Side from 1957 to 1959. These are not the chapter-length mathematical explorations from Mathematical Games but rather what one typically finds in a collection of brain teasers: items of one to two pages, essentially a word problem followed by an explanation of its solution. Altogether, there are about 60 puzzles in this book. They are arranged into ten categories such as money puzzles, speed puzzles, plane and solid geometry puzzles, and probability puzzles.

Compared to his writings for Scientific American, these little brain teasers are not Gardner’s best work. It’s amazing how many of these puzzles conclude with “Nope. It can’t be solved.” You read the first page, wrack your brain to try to come up with a solution, and then turn the page to find out there’s no viable answer. Where’s the fun in that? If it were one or two puzzles, that would be reasonable, but it seems like nearly half the book is unsolvable. Another frustrating aspect of brain teasers in general is that they are essentially mathematics written with words, and if the author isn’t exactly precise and clear in the wording of the problem, then you end up feeling like you’ve been cheated or you wasted your time. Gardner’s guilty of that as well in a number of these riddles. Such occasions call to mind the questions on your old school math tests that no one in the class got right because the teacher worded them poorly.

Nevertheless, there’s still fun to be had here and math to be learned. Every puzzle has its little twist that forces you to think outside the box of straightforward solutions. As the aforementioned list of categories indicates, there are little lessons on geometry, probability, and arithmetic. These are not easy math puzzles, but you don’t need to know algebra or calculus to figure them out. The most unfamiliar area for most will probably be the little section on topology. Gardner also describes some games of the abstract strategy variety (think checkers or tic tac toe, for example) that can be played with pencil and paper, coins, or other everyday items.

The material here may not be Gardner’s most ingenious writings, but this little book still does its job adequately. The next time I download a volume of Gardner’s mathematical puzzles, however, I’ll make sure it’s one of the 15 volumes from his Scientific American series.