Table Of ContentMATHEMATICAL
BRAINTEASERS
SURPRISING
with
SOLUTIONS
Owen O’Shea
Foreword by
Colm Mulcahy
Professor of Mathematics
Spelman College
Atlanta, Georgia
An imprint of The Rowman & Littlefield Publishing Group, Inc.
4501 Forbes Blvd., Ste. 200
Lanham, MD 20706
www.rowman.com
Distributed by NATIONAL BOOK NETWORK
Copyright © 2020 by Owen O’Shea
The names “Sam Loyd,” “Samuel Loyd,” “Cyclopedia,” “The Horse of a Different
Color,” and “Get off the Earth Paradox” are registered trademarks of The Sam Loyd
Company, TM & © and are used in this volume with the kind permission of
The Sam Loyd Company.
All rights reserved. No part of this book may be reproduced in any form or by any
electronic or mechanical means, including information storage and retrieval systems,
without written permission from the publisher, except by a reviewer who may quote
passages in a review.
British Library Cataloguing in Publication Information available
Library of Congress Cataloging-in-Publication Data
Names: O’Shea, Owen, 1956– author.
Title: Mathematical brain teasers with surprising solutions / by Owen O’Shea.
Description: Amherst, New York : Prometheus Books, 2020. | Includes bibliographical
references and index.
Identifiers: LCCN 2019016393 (print) | LCCN 2019017692 (ebook) |
ISBN 9781633885851 (ebook) | ISBN 9781633885844 (pbk.)
Subjects: LCSH: Mathematical recreations. | Word problems (Mathematics)
Classification: LCC QA95 (ebook) | LCC QA95 .O2727 2019 (print) |
DDC 793.74—dc23
LC record available at https://lccn.loc.gov/2019016393
The paper used in this publication meets the minimum requirements of American
National Standard for Information Sciences—Permanence of Paper for Printed Library
Materials, ANSI/NISO Z39.48-1992
To Dermot and Kathleen,
Tony and Nora,
Noreen and Jerry,
Oliver and Ann,
Ann and Con,
Teresa and Denis,
Breda and Frank,
My late sister-in-law, Vera,
and to my twin brother, Michael, and his son, Kevin.
CONTENTS
Foreword xi
Introduction xv
EASY PUZZLES, EASY TEASERS 1
1. The Rope Ladder 3
2. The Bottle and the Cork 5
3. The Newspaper Round 7
4. Cigarette Butts 9
5. Which Tank Will Empty First? 11
6. How Long Is the Line AB? 13
7. Blaney to Slaney 15
8. The Case of the Missing Dollar 17
9. How Long Is the Side of the Inner Square? 19
10. The Train Leaving and Returning to the Station 21
11. The Height of the Stack of Paper 23
12. The Caterpillar 25
13. Brooklyn versus Bronx 27
14. The Color of the Bear 29
15. 9 Coins 31
16. 2 Teenagers 33
17. The Unlucky Storekeeper 35
18. Bacteria in a Jar 37
19. 3 Cats 39
20. The Thief in the Store 41
21. Counting Blonde Students 43
22. The Cost of Shoeing a Horse 45
23. The 16-Inch Ruler 49
24. Pay Raise and Pay Cut 51
25. The Cleaning Lady 53
v
vi CONTENTS
CHALLENGING TEASERS 55
26. The Lonely Monk 57
27. The Town Council Clock 59
28. The Books on the Bookshelf 61
29. The Black and White Marbles 63
30. How Far Has the Fly Traveled? 65
31. 5 Loaves and 3 Gentlemen 67
32. 2 Red Queens and a Black Ace 69
33. The Curious Transaction That Resulted in a Missing Dollar 71
34. Counting the Number of Earrings 73
35. The Bicycle Race 75
36. The Will 77
37. The 2 Crossing Ropes 79
38. The 2 Bullets in a Revolver 83
39. The Bookworm 85
40. How Many Ways Can the 20 Numbers on a Dartboard
Be Arranged? 87
41. The Tower of Hanoi Puzzle 89
42. The Kidnapper 93
43. The 5 Letters and Envelopes 95
44. The Rate of Speed That Mary Swims 97
45. The Floating Ice Cube 99
46. The 10 Stacks of Coins 101
47. Signs along the Highway 103
48. Choose 2 Good Eggs from 6 105
49. The Party 107
50. Whom Should Johnny Play First? 109
51. The Engagement Ring 113
52. The 2 Women Selling Apples 115
53. Tommy Takes a Walk 119
54. The Story of Linda 123
55. The Problem of the Average Speed on the Round-Trip 127
56. Bixley to Quixley 129
57. The Boat and Its Cargo 133
58. The Mutilated Checkerboard 135
CONTENTS vii
59. The Rose Garden 139
60. The Deck of Cards Problem 143
61. The Weight of the Potatoes 145
62. Calculating the Width of a River 147
63. The Green and Blue Cabs 151
64. The 3 Dice 153
65. The 3 Vagabonds 155
66. The Tennis Tournament 157
67. 2 Footballs 159
68. The Birthday Paradox 161
69. The Second Child Puzzle 165
70. The 4 Bridge Players 169
71. The 2 End Digits of 20 Numbers 171
72. Lewis Carroll’s Problem in Probability 173
73. Against the Wind 175
74. The 2 Express Trains 177
75. The Man Packing a Suitcase 179
SLIGHTLY MORE CHALLENGING
TEASERS 181
76. The Links in the Gold Chain 183
77. The Rotating Coin 187
78. Dividing the Spoils 189
79. Counting the Votes 191
80. The Fence-Post Problem 193
81. Mr. Blueberry’s Will 195
82. The Jeweler and the Chain 197
83. The Price of a Book 199
84. Visiting a Friend 201
85. The Typing Teenager 203
86. Mr. Simpson’s Influence 205
87. The Potential Employee 209
88. The Price of Books 211
viii CONTENTS
89. The Lady in the Jewelry Store 213
90. Proving Dr. Krieger’s Equation Cannot Hold 215
91. The Problem Involving Percentages 217
92. The HIV Test 219
93. The Mammogram Test 221
94. Boys and Girls 223
95. The Distance to the Horizon 227
96. Traversing 50 Miles of Track 231
97. 2 Steamboats 233
98. The Bridge Players 237
99. The Most Likely Position of the First Black Ace
in a Shuffled Deck 241
100. Gold and Silver Coins 243
101. The Paradox of the Second Ace 245
102. The Pay Raise 249
103. The Daily Commuter 253
104. How Far Is It from Flag D to Flag A? 255
105. The 2 Tennis Players 261
106. The Courier Problem 265
107. The Lake Problem 269
108. The Spot in a Rectangle 273
109. How Should the Investment Be Divided? 277
110. Square Fields and Fence Hurdles 279
111. The Rope around the Earth 283
112. The Rope in the Soccer Playing Field 285
113. Which Scenario Should You Choose? 287
114. What Is the Probability That You Will Get Your Assigned Seat? 289
115. The Floating Hat 291
116. The 2 Riverboats 295
117. What Is the Largest Number That Can Be Expressed
Using 3 Digits? 299
118. Lottery Odds 301
119. Water and Brandy 303
120. The Hole through a Sphere 305
121. The Ant on a Rubber Rope 311
CONTENTS ix
SHORT BIOGRAPHIES 315
Samuel Loyd 317
Henry Ernest Dudeney 321
Martin Gardner 325
Notes 333
Select Bibliography 337
