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

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