Book:T.H. O'Beirne/Puzzles and Paradoxes

T.H. O'Beirne: Puzzles and Paradoxes

Published $\text {1965}$, Oxford University Press.

Subject Matter

• Recreational Mathematics

Contents

Acknowledgement

PREFACE

$1$. ONE MORE RIVER TO CROSS

Transport problems and imperial exercises

Three men and a boat -- not forgetting their wives

When valets or cannibals are second-class passengers

Tribulations of a family of five

Some statistics and other diversions

Boats and wolves and cabbages

How father can make his connexions

Odd paths for missionaries

On and on, up and up ...

A map is a help, if you can find one

$2$. FALSE COINS AND TRIAL BALANCES

A man of principle, and some others

False coins in two World Wars

Tempting, but wrong ...

Putting twelve coins through a sieve

False coins and the Cartesian Method

Three weapons against the coiner

About false coins, in double-column

When all suspicions point the same way

Three weighty trifles

Scales of other types, and how to use them

$3$. NEW WEIGHS WITH FALSE COINS

When you have nothing to weigh

Programmes and how they are numbered

How to make exceptions

A foolscap sheet to cover $120$ coins

You can do more if your balance has weights

How to exercise discrimination

False coins in ever-increasing numbers

A three-weight split of six coins

A spring-balance extension

A spring problem from Japan

$4$. JUG AND BOTTLE DEPARTMENT

Trials and errors of pourers of fluids

If you can't undo it, don't do it

Dividing fluids with triangle-mesh nets

A tetrahedron with every four containers

Problems for secret agents and others

When one measure of fluid will suffice

One-way traffic from a barrel

Barrels with unknown contents

How to avoid going round in circles

Customers who mix their drinks: a bartender's guide

$5$. A GAMUT OF GEOMETRY FROM $A$ TO $Y$

School geometry and a vicious circle

Making do with fewer points

The laws of the letters

Something to put on the wall

An incomparable arithmetic

Triangles old and new

Now you see it -- now you don't!

When twice as big is the same size

All this -- and comics too!

A different problem: or is it?

$6$. RACE-TRACK PROBLEMS AND LEGAL FICTIONS

Making the circuit of the race-tracks

A procedure of limited variety

Pointers towards a true direction

Legal fictions in correct perspective

Making the use of inside information

Putting it all on a rational basis

Not non-decimal, but undecimal

To higher dimensions, with Desargues

Best ways of getting the feel of it

Steps to take with yard-sticks and quadrants

$7$. CUBISM AND COLOUR ARRANGEMENTS

'Plus ça change --' : the Tantalizer through the ages

Try this -- it may well work!

Marshalling five Allied Flags, or more

How to use two chains if you can find them

Mutations and natural selection

Forming threes and forming fours

All or nothing in five-way agreements

Uses for non-standard dice

Addition sums as further complications

Don't just tumble them together!

$8$. GAMESMAN, SPARE THAT TREE

Games: and when they are impartial

Wythoff's game, and how to lose it

Never mind the fractions!

Contests of tree surgery

How best to split heaps unequally

Games for optimists and pessimists

Marks of favour and disfavour

What to do if you may want to lose

Nim -- for beginners

Nim -- for experts

$9$: 'NIM' YOU SAY -- AND 'NIM' IT IS

When no two are equal among four

The difference a fifth one can make

When you can put, as well as take

When only the odd ones matter

Nim-sums and faulty adders

When a heap is not a heap

How Nim-sums give the right labels

Developing a line of winning numbers

Take them, or split them -- just as you like!

How to divide and conquer

$10$. TEN DIVISIONS LEAD TO EASTER

Back rooms and their problems

Wheels within wheels within wheels

Numerical orthodoxies and heresies

Where the limits are set

Reformations and their problems

The tables of the law

Gaussian error and its correction

Commentary on a decalogue

Hard cases and bad laws

Future prospects for Easter

$11$. PROBLEMATIC LIES AND UNEXPECTED TRUTHS

Seeking unity in diversity

Four doubtful statements -- and a fifth

When everybody keeps to the point

Problems raised by irrelevant talk

Exercises, examinations, and executions

How the unexpected can always happen

Ways of dodging the real issue

Some circular arguments

Too good to be true?

Evil spells: and how to avoid them

$12$. A CHRISTMAS CRACKER WITH $100$ BIRDS

The start of the trail

Balancing cows against pigs

An Arab mathematician and his problems

A problematic medieval manuscript

Contracts and conflicts between East and West

One? More? Or none?

A count of $2,678$

Birds of China and India

A contour map of bird distributions

The end of the road

POSTSCRIPT

REFERENCES

INDEX

Cited by

• 1986: David Wells: Curious and Interesting Numbers