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Amusements in Mathematics
by
Henry Ernest Dudeney
Web-Books.Com

Amusements in Mathematics

Amusements in Mathematics.............................................................................................. 2

 

Units Abbreviation and Conversion.................................................................................... 4

 

Preface................................................................................................................................. 5

Arithmetical And Algebraical Problems............................................................................. 6
MONEY PUZZLES........................................................................................................ 6

AGE AND KINSHIP PUZZLES.................................................................................. 17
CLOCK PUZZLES....................................................................................................... 25
LOCOMOTION AND SPEED PUZZLES................................................................... 28

DIGITAL PUZZLES. ....................................................................................................... 30 VARIOUS ARITHMETICAL AND ALGEBRAICAL PROBLEMS......................... 37

Geometrical Problems....................................................................................................... 54
DISSECTION PUZZLES. ............................................................................................ 54
GREEK CROSS PUZZLES. ........................................................................................ 55

VARIOUS DISSECTION PUZZLES. ......................................................................... 62
VARIOUS GEOMETRICAL PUZZLES. .................................................................... 74

Points And Lines Problems............................................................................................... 83

 

Moving Counter Problems................................................................................................ 86

 

Unicursal And Route Problems ........................................................................................ 97

 

Combination And Group Problems ................................................................................ 104

Chessboard Problems...................................................................................................... 115
THE CHESSBOARD. ................................................................................................ 115
STATICAL CHESS PUZZLES.................................................................................. 118
THE GUARDED CHESSBOARD............................................................................. 126

NON-ATTACKING CHESSBOARD ARRANGEMENTS.................................. 127
THE TWO PIECES PROBLEM. ........................................................................... 128
DYNAMICAL CHESS PUZZLES. ........................................................................... 129

Measuring, Weighing, And Packing Puzzles.................................................................. 142

 

Crossing River Problems ................................................................................................ 146

 

Problems Concerning Games.......................................................................................... 149

Puzzle Games.................................................................................................................. 154 Magic Square Problems .................................................................................................. 157 SUBTRACTING, MULTIPLYING, AND DIVIDING MAGICS............................. 161 MAGIC SQUARES OF PRIMES. ............................................................................. 163

Mazes And How To Thread Them ................................................................................. 166

 

The Paradox Party........................................................................................................... 172

 

Unclassified Problems .................................................................................................... 182

 

SOLUTIONS 1-100 ........................................................................................................ 189

 

SOLUTIONS 101-200 .................................................................................................... 220

 

SOLUTIONS 201-300 .................................................................................................... 256 SOLUTIONS 301-430 .................................................................................................... 296

Units Abbreviation and Conversion

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 ¼ d. 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.

Preface

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 algebra. 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.

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 puzzles are capable of being solved by him on purely arithmetical lines.