OFFICIAL M E N S A PUZZLE
THE
BIG
BOOK
OF
PUZZLES
TERRY S T I C K E L S JAICO
THE BIG BOOK OF
MINDBENDING PUZZLES OFFICIAL MENSA PUZZLE
T E R R Y
BOOK
S T I C K E L S
m
J A I C O PUBLISHING HOUSE A h m e d a b a d Bangalore B h o p a l C h e n n a i Delhi Hyderabad Kolkata Mumbai
Published by Jaico Publishing House 121 Mahatma Gandhi Road Mumbai - 400 001
[email protected] www.jaicobooks.com © Terry Stickels Published in arrangement with Sterling Publishing Co., Inc. 387 Park Avenue South New York, NY 10016 T H E BIG B O O K O F M I N D - B E N D I N G P U Z Z L E S ISBN 978-81-7992-859-2 First Jaico Impression: 2008 N o part of this book may be reproduced or utilized in any form or by any means, electronic or mechanical including photocopying, recording or by any information storage and retrieval system, without permission in writing from the publishers. Printed by Anubha Printers B-48, Sector-7, Noida - 201301
INTRODUCTION . .5 PUZZLES
7
ANSWERS . . . .
231
INDEX
332
»
I n t r o d u c t i o n This collection of puzzles c o m e s from four previous books, with a sprinkling of new ones—all emphazizing the fun of thinking. You'll find everything from word to spatial/visual puzzles . . . from math to logic. I picked the puzzles I thought would offer you the best challenge and still put a smile on your face. I took the mission seriously. There are puzzles for the n e o p h y t e and for the v e r y best puzzle solvers. With ten different categories, no o n e will be shut out of enjoying his or her favorite puzzles. Now, it's your turn. Approach this v o l u m e in any manner that is comfortable. Skip around if y o u like. After, all this w h o l e effort is to entertain you. Let me know what you think. Send m e a note through my website at www.terrystickels.com. Have fun. —Terry
5
Stickels
PIJ^LES
1 For the uninitiated, the first three puzzles are called cryptarithms or, more precisely, alphametics. Puzzle creator J. A. H. Hunter coined the term alphametic to designate words that have meaning, rather than the random u s e of letters found in cryptarithms. The object of this type of puzzle is to replace letters with digits. Each letter must represent the same digit, and n o beginning letter of a word can be zero. If properly constructed, alphametics can be d e d u c e d logically. In the first puzzle, my verbal arithmetic leaves something to be desired. Assign a number to each letter to correct my addition. Hint: Make a box or chart to consider the possibilities of different values.
ONE ONE ONE +ONE TEN
NOON MOON +SOON JUNE
9
This third alphametic is more difficult than the first two, and there is more than one correct answer. Hint: create more than one chart of values.
THIS IS NOT +WITH WHICH U If B + P + F = 24, what are the values of Q and T? Hint: Consider whole numbers only.
A + B= Z + P= T+ A= F + S= Q-T =
Z T F Q 7
y
0
/ V A N '
X O
v A
X 0 X 0 0 X X X 0 0
r\
0
is The s u m of the infinite series
+ 'A + l k +
. . . equals 1.
What is the sum of the infinite series y4 + Vie + Ye4 + '/jse . . . ?
15
'i
19 This puzzle requires analytical reasoning. Determine the relationships b e t w e e n the figures and words to find t w o solutions.
RAB = o o
o o o = LAG 0 0 = LEB 0 0 0
=
0 REG = 0
?
0 REBRAG = ?
( 20 Here's another opportunity to u s e analytical reasoning, but this puzzle has a slightly different twist. In a foreign language: "Kafnavcki
roi" means "Take three pieces."
"Kir roi palt" means "Hide three coins." "Inoti kaf kir" means "Cautiously take coins." How would y o u say "Hide pieces cautiously" in this language?
'I 2 1 Seventy-eight percent of all p e o p l e are gum chewers, and thirty-five percent of all people are under the age of fifteen. Given that a person has been selected at random, what is the probability that the p e r s o n is not a gum chewer and above age fifteen?
16
What is the next letter in this series?
A
B
D
O
P
Q
?
< 23 A.
B.
(2 64
+
263
+
2 6 2 . . . 22
+
21
+
2°)
In comparing the values of A and B, which of t h e s e statements is correct? B is 2
64
larger than A.
64
A is 2
larger than B.
A and B are equal. B is larger than A by 1. A is larger than B by 1.
'i 24 Classic puzzles are fun to revisit now and then, especially if there's a new twist. In this puzzle, s e e if you can be as successful as John in retrieving water for his mother. The new twist? The buckets are different sizes. John's mother told him to go to the river and bring back exactly 9 gallons of water in o n e trip. She gave him a sixgallon bucket and a five-gallon bucket to complete his task. Of course, John's mother told him she'd bake his favorite cake if he came back with the 9 gallons. John had his cake and ate it, too. Can you?
17
125
1881:1961 - 6 0 0 9 :
?
i 26 In the world of physics, s o m e t i m e s things that appear t o m o v e forward are actually moving backward. Knowing this, can y o u complete this analogy?
EMIT : STAR :: TIME :
?
il 27 What is the next number in this series?
1
9
18
25
27
21
?
I 28 Nine men and s e v e n w o m e n pick as much corn in five days as s e v e n men and eleven w o m e n pick in four days. Who are the better corn pickers and by h o w much?
'i
29 Puzzles 29 to 35 are all c o m p o s e d of numbers, but that doesn't necessarily mean that the numbers contained in any given problem are mathematically related. Your mind will have to be flexible to determine what type of relationship the numbers in the series have with each other. There are n o holds barred, and e a c h puzzle may have a solution more obvious than you realize at first. What is the next number in this series?
1
2
4
13
31
18
112
?
>JU 30 What is the next number in this series?
1
4
2
8
5
7
?
Hint: This might be just a fraction of what you think.
9 3is the 15missing 7 12 5 What number in this 13 series?
17
M 32 What is the next number in this series?
0
2
4
6
8
12
12
20
16
SS 33 What is the missing number in this series?
16 21
26 26
12
?
19
ESS 34 What is the next number in this series?
3
4
11
16
27
36
?
US 35 What is the next number in this series?
224
1
8
30 19
5
?
11
No puzzle book would be c o m p l e t e without at least one anagram. Here is a phrase that, w h e n unscrambled, spells the name of a famous person. The phrase gives a small hint relating to the person's identity.
BEEN IN STAR LITE jgJK
:
?
)
Find the hidden phrase or title.
I 67 At a gathering of mathematicians, everyone shook hands with four other people, except for t w o people, w h o s h o o k hands with only one other person. If one person shakes hands with another, each person counts as one handshake. What is the minimum number of p e o p l e w h o could have been present? What is the total number of handshakes that took place?
Us You've just thrown your first t w o dice in a craps game and your point is 10. This means that you must continue to roU the dice until you roll another 10 to make your point. If y o u roll a 7 before you roll another 10, y o u lose. What are your chances of winning with 10 as your point?
34
The n u m b e r s 1 through 6 are arranged s o that any n u m b e r resting b e t w e e n and b e l o w t w o o t h e r n u m b e r s is t h e difference b e t w e e n t h o s e t w o numbers.
Using n u m b e r s 1 through 10, fill in t h e X's b e l o w t o create a "difference triangle" with t h e s a m e conditions. If you'd like a little stiffer challenge, try this using t h e n u m b e r s 1 through 15 in five rows.
X X X X 5 X X X 7 X 70 This puzzle is a variation of t h e g a m e nim, named b y Harvard m a t h e m a t i c s p r o f e s s o r Charles Bouton in 1901. Mathemagician Martin Gardner d i s c u s s e s a v e r s i o n of t h e game in his book Entertaining Mathematical Puzzles. In Gardner's version, c o i n s are arranged like this:
35
Two players take turns removing the coins. More than o n e coin can be removed on a turn as long as they are in the same row. The person w h o is forced to take the last coin is the loser. Gardner asks the reader if an ironclad winning first m o v e can be determined. The answer is yes. The first player removes three coins from the bottom row. In our version of nim, an extra coin is added to the top s o that the ten coins are arranged like this.
The rules are basically the same, except that in our game, if more than one coin is removed from any row, the coins must be adjacent to each other. For example, if a coin had been removed from the bottom row by a player, the other player may not pick up the remaining three coins.
removed
In this case, the s e c o n d player may pick up the coin on the left or either or both on the right. In our version, there are two winning first moves. What are they?
36
92 Logician George Summers's p u z z l e s are a m o n g t h e best. His logic brainteasers offer a clear, straightforward presentation of the puzzle, yet fully t e s t t h e d e d u c t i v e reasoning p r o c e s s of e v e n t h e best puzzle enthusiasts. His b o o k The Great Book of Mind Teasers
~iC
®o Bag 1
'
"'l
®© Bag 2
—
)
>
^
—
,y
V
Bag 3
75 Three straight cuts on a single plane through a cube will result in a maximum of eight pieces. What is the maximum number of pieces that will result when four planar cuts are made through a cube? The slices may not be rearranged between cuts.
39
>jg
