# Calculator's Cunning: The Art of Quick Reckoning

## Excerpt

An arithmetical trick is a device for solving a problem more easily and surprisingly than by ordinary methods. While one person will see behind it the broad and wonderfully intricate world of numbers, another will be satisfied by his delight in the trick itself. This book will serve both kinds of student. It will teach the beginner to master a series of useful methods and above all to look at the numbers before doing any calculation, in order to use the tricks appropriate to them; for the advanced student, and for anyone who enjoys numbers, it will afford many pleasant glimpses into the land of numbers, and stimulate him to a voyage of discovery.

Numbers have a certain magic. It is no accident that their wonderful properties have grown into the theory of numbers, 'the queen of mathematics'. Those relations which the schoolboy knows as arithmetical tricks belong to elementary number-theory.

Why this rather contemptuous term for sensible arithmetical devices? One reason is that they are nameless. There are no concise terms for the different examples, numbers, and methods, so that only the initiated learn these secrets, and the layman remains bewildered by them. For this reason, and so that they may remain alive, particularly in schools, these arithmetical devices will often be described by short, picturesque names and rules of thumb. A trick is killed off by a long-winded description.

Machine-calculation today stunts the growth of proper calculation, and therefore of number-sense, just as the motor-car stunts the growth of legs. In management and banking circles this is loudly lamented. As for calculating-machines, every teacher has experienced something of this sort: a sixth-former, faced with the exercise 2 x 2, gets out his slide-rule and gives the 'exact' answer 3·95. Every teacher also knows how efficiently the slide-rule can be combined with a well-developed facility in arithmetic.

This book, to which the introduction serves as a preliminary guide, will help to arouse and develop this facility, and to enable the reader to calculate more skilfully and enjoyably. It will also be a reference book for all teachers (including parents), in which they can learn the possibilities and methods of profitable arithmetic.

To calculate enjoyably—that sounds like aiming too high. But number‐ sense is more widely spread among the population than one would think, and often needs only a favourable impulse to awaken it.

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