Good Old Fashioned Challenging Puzzles and Perplexing Mathematical Problems (Puzzle Books) (Puzzle Books)
By Henry Dudeney
* Publisher: Summersdale Publishers
* Number Of Pages: 160
* Publication Date: 2007-02-12
* ISBN-10 / ASIN: 1840245573
* ISBN-13 / EAN: 9781840245578
* Binding: Paperback
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.
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. If
there were no puzzles to solve, there would be no questions to
ask; and if there were no questions to be asked, what a world it
would be! We should all be equally omniscient, and conversation
would be useless and idle.
It is possible that some few exceedingly sober-minded
mathematicians, who are impatient of any terminology in their
favourite science but the academic, and who object to the elusive
x and y appearing under any other names, will have wished that
various problems had been presented in a less popular dress
and introduced with a less flippant phraseology. I can only refer
them to the first word of my title and remind them that we are
primarily out to be amused—not, it is true, without some hope
of picking up morsels of knowledge by the way. If the manner is
light, I can only say, in the words of Touchstone, that it is ‘an illfavoured
thing, sir, but my own; a poor humour of mine, sir.’
As for the question of difficulty, some of the puzzles, especially
in the Arithmetical and Algebraical category, are quite easy. Yet
some of those examples that look the simplest should not be
passed over without a little consideration, for now and again it
will be found that there is some more or less subtle pitfall or
trap into which the reader may be apt to fall. It is good exercise
to cultivate the habit of being very wary over the exact wording
of a puzzle. It teaches exactitude and caution. But some of the
problems are very hard nuts indeed, and not unworthy of the
attention of the advanced mathematician. Readers will doubtless
select according to their individual tastes.
In many cases only the mere answers are given. This leaves the
beginner something to do on his own behalf in working out the
method of solution, and saves space that would be wasted from
the point of view of the advanced student. On the other hand,
in particular cases where it seemed likely to interest, I have given
rather extensive solutions and treated problems in a general
manner. It will often be found that the notes on one problem
will serve to elucidate a good many others in the book; so that
the reader’s difficulties will sometimes be found cleared up as
he advances. Where it is possible to say a thing in a manner that
may be ‘understanded of the people’ generally, I prefer to use
this simple phraseology, and so engage the attention and interest
of a larger public. The mathematician will in such cases have no
difficulty in expressing the matter under consideration in terms
of his familiar symbols.
I have taken the greatest care in reading the proofs, and trust
that any errors that may have crept in are very few. If any such
should occur, I can only plead, in the words of Horace, that ‘good
Homer sometimes nods,’ or, as the bishop put it, ‘Not even the
youngest curate in my diocese is infallible.’
I have to express my thanks in particular to the proprietors of
The Strand Magazine, Cassell’s Magazine, The Queen, Tit-Bits, and
The Weekly Dispatch for their courtesy in allowing me to reprint
some of the puzzles that have appeared in their pages.
THE AUTHORS’ CLUB
March 25, 1917
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