DENEY

In Mathematicks he was greater
Than Tycho Brahe or Erra Pater:
For he, by geometrick scale,
Could take the size of pots of ale;
Resolve, by sines and tangents, straight,
If bread or butter wanted weight;
And wisely tell what hour o' th' day
The clock does strike by algebra.

BUTLER'S _Hudibras_.

1917

PREFACE

In issuing this volume of my Mathematical Puzzles, of which some have
appeared in periodicals and others are given here for the first time, I
must acknowledge the encouragement that I have received from many
unknown correspondents, at home and abroad, who have expressed a desire
to have the problems in a collected form, with some of the solutions
given at greater length than is possible in magazines and newspapers.
Though I have included a few old puzzles that have interested the world
for generations, where I felt that there was something new to be said
about them, the problems are in the main original. It is true that some
of these have become widely known through the press, and it is possible
that the reader may be glad to know their source.

On the question of Mathematical Puzzles in general there is, perhaps,
little more to be said than I have written elsewhere. The history of the
subject entails nothing short of the actual story of the beginnings and
development of exact thinking in man. The historian must start from the
time when man first succeeded in counting his ten fingers and in
dividing an apple into two approximately equal parts. Every puzzle that
is worthy of consideration can be referred to mathematics and logic.
Every man, woman, and child who tries to "reason out" the answer to the
simplest puzzle is working, though not of necessity consciously, on
mathematical lines. Even those puzzles that we have no way of attacking
except by haphazard attempts can be brought under a method of what has
been called "glorified trial"--a system of shortening our labours by
avoiding or eliminating what our reason tells us is useless. It is, in
fact, not easy to say sometimes where the "empirical" begins and where
it ends.

When a man says, "I have never solved a puzzle in my life," it is
difficult to know exactly what he means, for every intelligent
individual is doing it every day. The unfortunate inmates of our lunatic
asylums are sent there expressly because they cannot solve
puzzles--because they have lost their powers of reason.