Amusements in Mathematics | Page 2

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, 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

CONTENTS
PREFACE v ARITHMETICAL AND ALGEBRAICAL PROBLEMS 1 Money Puzzles
1 Age and Kinship Puzzles 6 Clock Puzzles 9 Locomotion and Speed Puzzles 11 Digital
Puzzles 13 Various Arithmetical and Algebraical Problems 17 GEOMETRICAL
PROBLEMS 27 Dissection Puzzles 27 Greek Cross Puzzles 28 Various Dissection
Puzzles 35 Patchwork Puzzles 46 Various Geometrical Puzzles 49 POINTS AND LINES
PROBLEMS 56 MOVING COUNTER PROBLEMS 58 UNICURSAL AND ROUTE
PROBLEMS 68 COMBINATION AND GROUP PROBLEMS 76 CHESSBOARD
PROBLEMS 85 The Chessboard 85 Statical Chess Puzzles 88 The Guarded Chessboard
95 Dynamical Chess Puzzles 96 Various Chess Puzzles 105 MEASURING, WEIGHING,
AND PACKING PUZZLES 109 CROSSING RIVER PROBLEMS 112 PROBLEMS
CONCERNING GAMES 114 PUZZLE GAMES 117 MAGIC SQUARE PROBLEMS
119 Subtracting, Multiplying, and Dividing Magics 124 Magic Squares of Primes 125
MAZES AND HOW TO THREAD THEM 127 THE PARADOX PARTY 137
UNCLASSIFIED PROBLEMS 142 SOLUTIONS 148 INDEX 253

AMUSEMENTS IN MATHEMATICS.

ARITHMETICAL AND ALGEBRAICAL PROBLEMS.
"And what was he? Forsooth, a great arithmetician." Othello, I. i.
The puzzles in this department are roughly thrown together in classes for the convenience
of the reader. Some are very easy, others quite difficult. But they are not arranged in any
order of difficulty--and this is intentional, for it is well that the solver should not be
warned that a puzzle is just what it seems to be. It may, therefore, prove to be quite as
simple as it looks, or it may contain some pitfall into which, through want of care or
over-confidence, we may stumble.
Also, the arithmetical and algebraical puzzles are not separated in the manner adopted by
some authors, who arbitrarily require certain problems to be solved by one method or the
other. The reader is left to make his own choice and determine which