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

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T.H. O'Beirne: Puzzles and Paradoxes

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


Subject Matter


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 ├ža 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


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