Transcribers note: Many of the puzzles in this book assume a familiarity with
the currency of Great Britain in the early 1900s. As this is likely not common
knowledge for those outside Britain (and possibly many within,) I am including a
chart of relative values.
The most common units used were:
||abbreviated: d. (from the Roman penny,
There was 12 Pennies to a Shilling and 20 Shillings to a Pound, so there was
240 Pennies in a Pound.
To further complicate things, there were many coins which were various
fractional values of Pennies, Shillings or Pounds.
|Sixpence (or tanner)
|Shilling (or bob)
|Florin or two shilling piece
|Half-crown (or half-dollar)
|Crown (or dollar)
|Sovereign (or Pound)
||£1 or 20s.|
This is by no means a comprehensive list, but it should be adequate to solve
the puzzles in this book.
In Mathematicks he was
Than Tycho Brahe or Erra
For he, by geometrick
Could take the size of pots of
Resolve, by sines and tangents,
If bread or butter wanted
And wisely tell what hour o' th'
The clock does strike by
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. 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
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 ill-favoured thing, sir, but my own; a poor humour of mine,
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
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