Amusements in Mathematics

Henry Ernest Dudeney
Amusements in Mathematics

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Title: Amusements in Mathematics
Author: Henry Ernest Dudeney
Release Date: September 17, 2005 [EBook #16713]
Language: English
Character set encoding: ISO-8859-1

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[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
The most common units used were:
the Penny, abbreviated: d. (from the Roman penny, denarius) the Shilling, abbreviated: s.
the Pound, abbreviated: £
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.

Farthing ¼d.
Half-penny ½d.
Penny 1d.
Three-penny 3d.
Sixpence (or tanner) 6d.
Shilling (or bob) 1s.
Florin or two shilling piece 2s.
Half-crown (or half-dollar) 2s. 6d.
Double-florin 4s.
Crown (or dollar) 5s.
Half-Sovereign 10s.
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.
Exponents are represented in this text by ^, e.g. '3 squared' is 3^2.
Numbers with fractional components (other than ¼, ½ and ¾) have a + symbol separating
the whole number component from the fraction. It makes the fraction look odd, but yeilds
correct solutions no matter how it is interpreted. E.G., 4 and eleven twenty-thirds is
4+11/23, not 411/23 or 4-11/23.

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
BUTLER'S Hudibras.


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 idle.
It is possible that some
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