by Dudeney, Henry Ernest, 1857-1930
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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 Marc/7 25,1917
CONTENTS
PREFACE y
ARITHMETICAL AND ALGEBRAICAL PROBLEMS. 1
Money Puzzles. 1
Age and Kinship Puzzles. 6
Clock Puzzles. 9
Locomotion and Speed Puzzles. V\_
Digital Puzzles. 13
Various Arithmetical and Algebraical Problems. 17
GEOMETRICAL PROBLEMS. 2Z
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. Z6
CHESSBOARD PROBLEMS. 85
The Chessboard. 85
Statical Chess Puzzles. 88
The Guarded Chessboard. 95
Dynamical Chess Puzzles. 96
Various Chess Puzzles. 112
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
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.
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 puzzles are capable of being solved by him on purely arithmetical lines.
MONEY PUZZLES.
"Put not your trust in money, but put your money in trust." OLIVER WENDELL HOLMES.
1.?A POST-OFFICE PERPLEXITY
