Figures for Fun: Stories, Puzzles and Conundrums
Yakov Isidorovich Perelman (1882-1942) was a USSR science writer who wrote many popular physics and mathematics books. He died of starvation in Leningrad during the German siege. He is not related to the Fields Medal winner Grigori Perelman for solving the Poincaré conjecture. But the latter claims that he got interested in mathematics because his father gave him a book by Yakov Perelman.
His books Physics for Entertainment and Astronomy for Entertainment and some others are freely available on the Internet Archive. Also his Mathematics Can be Fun is available there. The latter consists of two parts: Figures for fun. Stories, puzzles and conundrums, and Algebra Can Be Fun. Although in a different edition in the Archive, the first part corresponds to the present booklet. This Dover publication of 2015 is an unabridged reproduction of the Frederik Ungar edition of 1965.
The booklet consists of some hundred witty tricks, puzzles and stories. Few are classics but most of them are originals that I did not see before. The problems are most often presented in a story telling form complete with dialogues and surprised characters when the ending turns out to be unexpected. The stories are very diverse. There are stories to make it clear to an unexperienced reader how amazingly fast exponential growth is. Starting with a small number, doubling it in every step soon leads to dazzling large numbers. Similarly factorials and combinatorics easily lead to a quite large number of possibilities. Other tricks are based on counting and explain to the reader how he or she can perform some act and amaze the public with what seems to be clairvoyance. But there are also very simple and practical guidelines to count for example the number of different species in a large mixture, or how to count using your fingers or measuring using body parts. The geometrical puzzles probably require some more thinking. For example, a fly sitting on the outside of a cylindrical glass spots a drop diametrically across the glass but on the inside. What is the shortest path the fly should run to get to the drop? Others have a physical flavour: can one compute the number of raindrops in an amount of water or the water level resulting from snow melting, or how impossible is the deluge as it is described in the bible?
The solutions and explanations are all included, sometimes following in a separate section, and sometimes they are part of the story. This a very entertaining booklet that will probably make you look for other books by Yakov Perelman. His physics book has a similar flavour and is certainly as pleasant to read as this one.