Mathematical Puzzles and Curiosities

135 Pages·2013·3.61 MB·English

by  Barry R. Clarke

“A thoroughly enjoyable and mind-expanding array of puzzles and curiosities”
Dr Cliff Pickover, author of Archimedes to Hawking
“Clever, original brain-teasers are rare. This book has some beauties. Very satisfying.”
Will Shortz, Crossword Editor, The New York Times
“I highly recommend this delightful book. It contains not only excellent puzzles, but also extremely
interesting commentaries and anecdotes.”
Professor Raymond Smullyan, author of To Mock a Mockingbird
“A wide-ranging and attractive collection that will appeal to all puzzle fans”
Professor Ian Stewart, author of Professor Stewart’s Cabinet of Mathematical Curiosities
“A masterpiece ... reminds me somewhat of my first introduction to Martin Gardner ... this is a must for all
puzzle lovers worldwide”
Terry Stickels, author of Frame Games
MATHEMATICAL
PUZZLES
&
CURIOSITIES
Barry R. Clarke
DOVER PUBLICATIONS. INC
Mineola, New York
Acknowledgments
I should like to thank Denis Borris and Mark Rickert for testing some of the
mathematics and logic puzzles in this work on the puzzles forum of my website
http://barryispuzzled.com. Also, thanks to my many mathematics students for
trying out some of the creative thinking puzzles and providing valuable
feedback. I am grateful to Val Gilbert, and Alex and Kate Ware, for providing
the opportunity to construct some of these puzzles for The Daily Telegraph.
Finally, I am grateful to Rochelle Kronzek and James Miller from Dover
Publications for their commitment to this work .
Copyright
Copyright © 2013 by Barry R. Clarke
All rights reserved.
Bibliographical Note
Mathematical Puzzles and Curiosities is a new work, first published by Dover Publications, Inc., in 2013.
International Standard Book Number
eISBN-13: 978-0-486-31572-0
Manufactured in the United States by Courier Corporation
49091201 2013
www.doverpublications.com
Contents
Introduction
The Monty Hall Problem
Mathematical Puzzles I
1. The Baffled Brewer
2. Horse Play
3. Court Out
4. Back to Class
5. Sound Arithmetic
6. Digital Dilemma.
7. Core Conundrum
8. Word in the Stone
9. The Backward Robber
10. Maximum Security
Judgment Paradoxes
Finger Multiplication
Creative Thinking Puzzles I
11. Mad House
12. Right Angle
13. Amazing
14. The Dead Dog.
15. Sum Line
16. Which Way?
17. Nothing for It
18. Rough Graph
19. The Lighthouse
20. The Pig and the Bird
The Sleeping Beauty Problem
Logic Puzzles
21. Shilly Chalet.
22. The Five Chimneys
23. A Pressing Problem
24. Alien Mutations
25. Santa Flaws
26. Safe Cracker
27. A Raft of Changes.
Parity Tricks with Coins
The Shakespeare Puzzles.
Creative Thinking Puzzles II
28. Inspector Lewis
29. The Builder’s Problem
30. The Four Dice
31. Politically Correct
32. Inklined
33. Bubble Math.
34. Arithmystic
35. No Escape
36. Secret City
37. Winning Line
The Hardest Ever Logic Puzzle
Zeno and Infinitesimals
Mathematical Puzzles II
38. The Striking Clock
39. Square Feet with Corn.
40. The Broken Ruler
41. Play on Words
42. Fare Enough
43. Having a Ball
44. Oliver’s Digeridoo
45. Neddy’s Workload
46. Armless Aliens.
47. The Slug and the Snail
The Unexpected Hanging
The Wave-Particle Puzzle
Creative Thinking Puzzles III
48. Moving Clocks
49. Miserable Marriage
50. Out of this World
51. Doubtful Date
52. Door to Door
53. No Earthly Connection
54. Water Puzzle.
55. Doing a Turn
56. The Tin Door
57. Fish Feast
58. Dig It
59. The Concealed Car
60. Pet Theory
Titan’s Triangle.
Creative Thinking Hints
Solutions
Introduction
First, here’s a little enigma which at first sight seems trivial, but if you keep
strictly to the given condition for solving it, then it’s not so easy. Below are
seven letters that form an anagram — and a seven-letter anagram is reasonably
straightforward — but the puzzle is, how can you reach the solution without
rearranging the letters? The answer, given at the end of the Introduction,
demands a leap of the imagination but remember, if you succumb to the
temptation to move the letters around then you’ve cheated!
So, welcome, and I hope that you enjoy this original collection of puzzles and
articles. It is a carefully considered compilation in which you can find
conundrums in logic, mathematics, and creativity, together with some thought-
provoking articles in recreational mathematics and philosophy. It is ideal for
those who enjoy alternative ways of thinking and who like to consider a fresh
approach to problems. Most of the book requires no specialised mathematical
knowledge but those articles near the end that are more demanding can be
penetrated by a reasonable amount of high-school algebra.
Some of the articles deal with classic teasers such as The Unexpected
Hanging, The Monty Hall Problem, and The Sleeping Beauty Problem, but I
have resisted resurrecting a standard analysis of these items, preferring instead to
present my own way of understanding them. Other topics such as the
Shakespeare Puzzles and Titan’s Triangle are entirely new, the first being a
creative interpretation of the dedications that preface the Shakespeare Sonnets
(1609) and First Folio (1623), and the latter being a fascinating extension of a
classic IQ puzzle. There are also more philosophical topics such as Zeno and
Infinitesimals, and the Wave-Particle Puzzle, which I hope will encourage the
reader to think again about these problems.
The puzzles in this work are entirely original and most of them have been
published in my column in The Daily Telegraph. They have been arranged to
increase in difficulty as the pages turn and the solutions have been deliberately
placed out of order at the end to avoid inadvertently seeing the next solution.
The answer to a puzzle can be located by referring to the solution number given
at the end of the puzzle (not the page number) then looking it up at the back of
the book. The creative thinking puzzles encourage alternative ways of thinking
and two hints for each are provided near the end of the book to lessen the
demand for mind reading. They are ideal for group problem-solving sessions and
many of them have already been tested on students who have found them
engaging, stimulating, and often amusing. If the solution remains beyond your
grasp, even after pondering the hints, please don’t feel frustrated. My wish for
you is that on examining the answer you can enjoy it as puzzle art and, perhaps
after having mastered a few of the basic principles, might even be inspired to
create some of your own.
The following is an example of the kind of visual creative thinking puzzle that
might be encountered within these covers. The solution is given at the end of the
Introduction. Can you spot the difference between these two quarters?
Having taught mathematics at various independent sixth-form colleges in
Oxford for many years, one of my interests is in the role that puzzles, especially
creative thinking ones, can play in developing the young mind. Sadly, the sole
aim of our education system as it currently stands is entirely materialistic, this
being to prepare students to obtain employment and earn a living. This usually
requires qualifications such as a school certificate or university degree and our
current school education system is one part of the long conveyor belt that serves
this end. Of course, there are bills to pay so earning a living is far from being
undesirable, but my point is that if this is the only goal then there is a price to
pay.
When the teacher of mathematics presents his material, he does so with the
intention of enabling his students to pass examinations. Mathematics
examinations consist of questions and each question demands one or more
methods to successfully negotiate it. If the student can identify the set of
techniques required for each particular problem and accurately apply them then
he can obtain a good result in the examination. The inquisitive student might
express reservations about the usefulness of a particular problem to his future
existence, ask for an insight into the history of the development of a certain