Introduction

It is usual for non-mathematicians to make rapid disclaimers
at the mere mention of anything mathematical; yet, at the
same time, many will derive great satisfaction from the solving
of puzzles which involve numerous mathematical principles.

Everyone must, at some time or other, make use of num-
bers. A business man may employ a cost accountant to amass
and construe volumes of statistics, and a sultan may delegate
to his vizier the delicate task of counting his wives; but
neither of them can wholly dispense with the processes of
counting. Similarly, the shopper who cannot add two figures
together on paper is still acutely number-conscious; she will
certainly not be satisfied with four bananas if she has paid for
five, nor will she be slow to observe and comment upon any
discrepancies in her change.

Numbers are, in fact, the concern of everybody in everyday
use, and it is for that reason that the present book is intended
for the general public rather than for any particular class of
reader. It is not in any way designed as a text-book. Instead,
it sets out to show, in a simple form, the ways in which
numbers, or groups of numbers, are related to each other;
how they can be expressed in terms of each other; and the
general nature of number behaviour in varying circum-
stances. It is, in short, an attempt to justify the fascination
which numbers exercise over the mind of the student who is
prepared to delve into and search out their characteristics.
In order to achieve this, a number of detailed explanations of
relationships—too often taken for granted—are included.

It is, of course, impossible to divorce one branch of mathe-
matics from other branches. Even if this were possible, how-
ever, it would still be undesirable, and far from attempt-
ing the impossible, it has been found necessary in certain

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