Those puzzling Japanese

Press, 19 December 1981, Page 18

Those puzzling Japanese

The Tokyo Puzzles. By Kobon Fujimura. Frederick Muller, London, 1981. 184 pp. $7.75 (paperback). (Reviewed by David Robinson) It is a test of any puzzle book that it should contain some puzzles that stump the reader so far that he says “That is impossible!", but when he turns to the solutions he should say “Of course! Why didn't I think of that?" This book passes that test. The puzzles are attractively set out. and are numbered up to 98. But there are really more than that, for some are chains of puzzles, and some will suggest to the reader a whole sequence of puzzles that he can devise and solve for himself. One, for example, involves the lifts in a tall building, which do not stop at every floor, but are so organised that for any two floors there is a lift that stops at both. I can imagine myself spending days looking at the variants of such a problem. How many lifts for example, would you need in a 12-storey building if every pair of floors was to be linked by a lift which did not stop anywhere in between? The great majority of the puzzles in this book were new to me, some were even of unfamiliar types. Many had a Japanese touch, but not of the kind that requires any knowledge of Japan to make them enjoyable, or solvable. The mathematical flavour, generally geometrical; often also combinatorial ("in

how many ways can you ...") is strong. There are a dozen puzzles concerning geometrical figures made , with matchsticks. Some, such as dividing a figure into two parts with equal areas using a fixed number of matchsticks, require considerable insight for their solution. It is pleasing to note that there are often several correct answers, since mathematics tends to suffer from the prejudice that there can only be one right answer, a state of affairs false in large parts of the subject. In his' introduction Martin Gardner quotes Fred Hoyle as claiming that mathematics should never be taught: students must learn for themselves, bysolving puzzles. While I would not go that far, puzzle books such as this can have an important place in the learning of mathematics. They do require some mathematical techniques and formal knowledge, but most of all they get the student away from the easier’, but ultimately boring path of learning to solve familiar problems by-reflex action. Faced with a puzzle such an approach is fatal. Each new puzzle requires us to go back to the beginning, to cast around for any-method to attack the problem. Ingenuity is the key. and I do not think it can be taught, only fostered. The solutions are given in pleasing detail, so that the train of argument can often be observed.