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

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## T.H. O'Beirne:

## 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 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