mind bending puzzles 1.pdf
TRANSCRIPT
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1RANE GAMES
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Published by Pomegranate Communications, Inc.
Box 6099, Rohnert Park, California 94927
Pomegranate Europe Ltd.
Fullbridge House, Fullbridge
Maldon, Essex CM9 4LE, England
1998 Terry Stickels
No part of this book may be reproduced or transmitted 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 copyright holders.
Pomegranate Catalog No. A505
ISBN 0-7649-0690-9
Designed by Harrah Argentine
Printed in U.S.A.
07 06 05 04 03 02 010 0 99 98 10 9 8 7 6 5 4 3 2
First Edition
Terry Stickels's Mind-Bending Puzzles are also available in calendars and decks of Knowledge
Cards, and in the book Mind-Bending Puzzles Volume II, all published by Pomegranate
Communications, Inc. For more information, please write to Pomegranate at Box 6099,
Rohnert Park, CA 94927; 800-227-1428 (www.pomegranate.com) .
http://www.pomegranate.com/http://www.pomegranate.com/ -
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F o r e w o r d
MOST OF THE NEW puzzle books that seem to be proliferating rapidly these days
consist mainly of old chestnuts refurbished with different story lines.Terry
Stickels's book, whi ch you now hold, is no t of this sort . W i t h f ew exceptions, the
problems he gives are his ownproblems not to be found in other collections.
A second meri t of this bo ok is that its puzzles avoid t w o extremes: they are
neither so difficult that general readersones with no knowledge of advanced
mathwill be unable to solve them, nor so simple that their solutions are obvi-
ous.To enjoy this collection all you need to know is basic arithmetic.
A thi rd me rit is tha t interspersed amon g th e mathematical teasers are wo rd
puzzles of a type that has been called a "w or dl e" a co mm on phrase symbolized
by an unusual way of printing words.They are fun to solve, and even more fun
to invent.
Th e greatest pleasure to be deri ved f rom a col lection such as this is to use
your will power to refrain from turning too quickly to the answers.Try your best
to solve each puzzle before you peek at its solution.
Allow me to close with a little novelty of my own. Printed below is a word
expressing my reaction to this book. It is written in a curious code.To decipher it,
hold this page upside down in front of a mirror
q G n a p x t n r
Martin Gardner
For more than twenty-five years, Martin Gardner wrote the "Mathematical Games" column in Scientific
Americancolumns now collected in fifteen books. His more than sixty other books include The New
Ambidextrous Universe, The Whys of a Philosophical Scrivener, The Night is Large, and Visitors from Oz.
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Welcome!
The puzzles in Mind-Bending Puzzles Volume I have been carefully picked t o for m
a selection that will b ot h challenge and ente rta in you. My aim is t o create puzzles
that you can enjoy solving without getting bogged down by complex approaches
and equation s.Th e puzzles offe red h er e "F ra me Games," visual /spatial puzzles,
w o r d and ma th pr oble ms, series puzzles, and logic pr ob le ms v ar y in difficulty, but
each on e was chosen t o exercise a diffe rent aspect of pr ob le m solving.There's
something here for everyone.
Th e publishers and I are always happy to hear f rom you, so please wr it e to usif yo u have any com men ts , criticisms, o r quest ions ab ou t these puzzles. Your con -
tinuing support for the Mind-Bending calendars and decks o f Kno wle dge Cards
produced by Pomegranate each year has made the publication of this book a
reality and has been enormously gratifying to me.
So than k y o u I ho pe you'l l have fun wit h Vo lu me I. Sharpen yo ur pencils,
and good luck!
Te r r y Stickels
PS. You'll find the answers on pages 85 - 93 in th e back of th e bo ok , along w it h
several "scribble pages" for your convenience.
Write to Terry do Pomegranate Communications, Inc., Box 6099, Rohnert Park, California 94927.
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Mind-Bending Puzzles I
Three dollar bills were exchangedfor acertain number ofnickels and the
same numberofdimes. How many nickels were there? Read this puzzleto
a groupof friends and see how longittakesto come up with the answer.
You maybesurprised!
In the multiplication puzzle below,x,y,and 2r represent different digits.
What isthe sumofx, y,andz\
yx
7
r y r y
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Mind-Bending Puzzles I
There is acertain logic shared by the following four circles. Can you deter-mine the missing number inthe last circle?
6.Let's say26zips weigh as much as4crids and2wobs.Also,8zips and2
crids have the same weight as2wobs. How many zips have the weight
of I wob?
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Mind-Bending Puzzles I
Find the hidden phraseortitle.
B S D 8 .
Can you determine the
A C
next letter inthe following series?
F H K M ?
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Mind-Be nding Puzzles I
What is Vi of 2/3 of 3/s of 240 divided by Vi?
1 0 .
One of the figures below lacks a common characteristic that the other 5
figures have.Which one is it and why?
WA/m
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Mind -Bending Puzzles I
I I .
A car travels from pointA topointB (adistanceofone mile)at 30milesper
hour. How fast would thecar haveto travel from point BtopointC (alsoa
distanceofone mile)toaverage60miles per hour for the entire trip?
1 2 .
Find the hidden phraseortitle.
12
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Mind-Bending Puzzles I
13.
The design on the leftismade upofthree paper squaresofdifferent sizes,
one on topofthe other.What is the minimum numberofsquares needed
to create the design on the right?
The three words below canberearranged into two words that are also
three words! Can you decipher this curious puzzle?
the red rows
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Mind-Bending Puzzles I
1 5 .
If a rectangle's lengthisincreased by25percent and its width isdecreasedby25percent, what is the percentageofchange inits area?
1 6 .
A friend hasabag containing two cherry gumdrops and one orange gum-
drop. She offerstogive you all the gumdrops you want ifyou can tellher
the chancesofdrawingacherry gumdropon the first draw and the orange
gumdropon the second draw Can you meet your friend's challenge?
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Mind-Bending Puzzles I
1 7 .
Try your luckatthis "trickle-down" puzzle. Startingatthe top, change oneletterofeach succeeding word toarriveatthe wordatthe bottom.
TOOK
BURN
1 8 .
Find the hidden phraseortitle.
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Mind -Bending Puzzles I
1 9 .
Given the initial lettersofthe missing words, complete this sentence.
There are 100 Yin a C.
IfI tripled one-quarter ofa fraction and multiplied itby that fraction,I
would get one-twelfth.What is the original fraction?
16
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Mind-Bending Puzzles I
21.Two toy rockets are heading directlyforeach other. One is travelingat 50
miles per hour and the other is travelingat 70miles per hour. How far
apart will these two rocketsbe one minute before they collide?
22.
Here'sa variation on an old classic. On what sideofthe line does the
"R" go?
A B D O P Q
C E F G H I J K L M N
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Mind-Bending Puzzles I
23.
Find the hidden phraseortitle.F R A M E
IG A M E
24.
Below are five words. By adding the same three lettersatthe beginningof
each word, you can come up with five new words.What three letters will
do the trick?
Her
Ion
Or
If
To
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Mind-Bending Puzzles I
25.
What is 10 percentof90 percentof80 percent?
26.Ifx2 islarger than 9, whichofthe following is true?
a. x is greater than0.
b. 0 is greater than x
c. x isequalto 0.
d. x3 is greater than0.
e. There isinsufficient information todetermineasolution.
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Mind -Bending Puzzles I
27.
Thinkof five squares that are the same size. In how many ways can thesefive squaresbecombined, edgetoedge?(Nomirror images allowed.)
28.Find the hidden phraseortitle.
20
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Mind-Bending Puzzles I
29.
Based on the following information, how many pleezorns does AhmadAdziz have?
Molly O'Brien has22pleezorns.
Debbie Reynolds has28pleezorns.
Roberto Montgomery has34pleezorns.
30.
A mixtureofchemicals costs $40 per ton.It iscomposedofone typeof
chemical that costs $48 per ton and another typeofchemical that costs
$36 per ton. In what ratio were these chemicals mixed?
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Mind-Bending Puzzles I
31.
Find the hidden phraseortitle.
32.
How many trianglesofany size are inthe figure below?
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Mind-Bending Puzzles I
33.
Decipher the following cryptogram:
WLA'P XLJAP RLJO XGMXBSAE NSQLOS PGSR GCPXG.
34.
If the ratioofSxtoAyis7 to8, what is the ratioof IOx to14y>
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Mind-Bending Puzzles I
35.
Below are four setsof letters that are related in away knowntovirtuallyeveryone. Can you find the missing two letters? (Hint: Some people have
been knownto take monthstosolve this!)
O N
DJ
FM
AM
? ?
36.
Find the hidden phraseortitle.
F R A M E
G A M E
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Mind-Bending Puzzles I
37.
How many four-letter words can you find inthe word "twinkle'(Try foratleast15.)
38.
What are the two missing numbers inthe series below?
8, 15, 10, 13, 12, I I , 14,9, 16,7, ?,?
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Mind-Bending Puzzles I
39.
Do this quickly: Write down twelve thousand twelve hundred twenty-two.
40.
Find the hidden phraseortitle.
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Mind-Bending Puzzles I
41.
What number is four times one-third the number that is one-sixteenthless than three-thirty-seconds?
42.
In the strange land of Doubledown the alphabet appears to be hieroglyph-
ics, but it isn't really much different from ours. Below is one of the
Doubledown months spelled out. Which month of ours is comparable?
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Mind-Bending Puzzles I
43.
Find the hidden phraseortitle.
44.
F R A M E
I
Sandwich
G A M E
Quickly now, which islarger, 267orthe sumof266 +265? How about267
or the sumof266 +266>
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Mind -Bending Puzzles I
45.
Unscramble this word:
GORNSIMMAROCI
46.Given the initial lettersofthe missing words, complete this sentence.
There ison e W ona U.
29
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Mind-Bending Puzzles I
47.
Below aresixrays. Choosing twoofthe rays, how many anglesofless than90 degrees can you form? (Angle ACB isless than90degrees.)
C
48.
By arranging all nine integers in acertain order,itis possibletocomeup
with fractions equalto '/2, '/3,lA, !/s,!/6,' A !/s,and 'ASeeifyou can come
up with oneofthese.
Example: J_ = 3,187
8 = 25,496
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Mind-Bending Puzzles I
49.
Find the hidden phraseortitle.
ISO.
What is the valueofz\r\ the following problem? (Each number isapositive
integer between0and9.)
y+z
xy
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Mind -Bending Puzzles I
51.
Referring backtothe last puzzle, where 2rwas foundto be9, what isthe
valueofxl
x
y+ z
xy
52.
Mostofus know the following rulesofdivisibility:
A number isdivisible by2 if itendsinan even digit.
A number isdivisibleby 3 ifthe sumofits digitsisdivisibleby 3.
Is there sucharulefordividing by 8?
32
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Mind-Bending Puzzles I
53.
Which oneofthe following five words doesn't belong with the others,
and why?
Pail
Skillet
Knife
Suitcase
Doorbell
54.
Fourof the figures below shareacharacteristic that the fifth figure doesn't
have. Can you determine which figure doesn't go with the others and why?
I X ? ) o ^ K o ,
A B C D E
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Mind -Bending Puzzles I
55.
Find the hidden phraseortitle.
56.
A certain barrelofcandy canbeequally divided (without cutting pieces)
between five, seven,orthirteen people.What is the least numberofpieces
of candy the barrel could contain?
34
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Mind -Bending Puzzles I
57.
If you wrote down all the numbers from5 to83, how many times would
you write the number 4?
58.Find the hidden phraseortitle.
F R A M E
BLANKfill
BLANKfill
BLANK
G A M E
35
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Mind -Bending Puzzles I
59.
Which is greater, 107 percentof300or 50percentof600?
60.What is the valueofthe following?
3 +3 ' / 3
36
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Mind-Bending Puzzles I
61.
The diagram below is the beginningofa "magic square" inwhichallrowsand columns and both diagonals add upto34. Can you fillinthe restof
the numbers?
1 8 13 12
144 1615
62.Find the hidden phraseortitle.
F R A M E
1"F3G A M - E
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Mind-Bending Puzzles I
63.
The diagram below canbedrawn without lifting your pencilorcrossingany other line. Can youdo it?
Imagine thatacoin called a "kookla" isequal invaluetoeither 7gold
piecesor 13silver pieces.Ifyou have40kooklas that you wantto
exchangeforboth silver and gold pieces and your bank has only 161 gold
piecesonhand, how many silver pieces should you expecttoreceive with
the 161 gold pieces?
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Mind-Bending Puzzles I
65.
The two numbers ineach box have the same relationshiptoeach other asdo the two numbers inevery other box.What is the missing number?
66.There are six chairs, eachofa different color. In how many different ways
can these six chairsbearranged in astraight line?
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Mind-Bending Puzzles I
67.
Find the hidden phraseortitle.F R A M E
| ONE
G A M E
H I 68.Unscramble the following word:
R G A A L E B
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Mind -Bending Puzzles I
69.
Do the numbers9and 10 go aboveorbelow the line?
3 4 5 7 8
70.
Find the hidden phraseortitle.
41
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Mind -Bending Puzzles I
71.
A concept that math students often find difficulttounderstand is thatanegative multiplied byanegative results in apositive (example: -5 -5 = 25).
Can you come up withareal-life example, in words, to illustrate this?
72.
Without using+ or -signs, arrange five 8s so that they equal9.
42
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Mind-Bending Puzzles I
73.
How many individual cubes are inthe configuration below? (All rows andcolumns runtocompletion unless you see them end.)
74.
How many different words can you make from the word "Thanksgiving"?
You mightbesurprisedto find how many new words canbemade froma
word that doesn't contain the letter "e."
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Mind -Bending Puzzles I
75.
Find the hidden phraseortitle.
76.
What isV\odividedbyVi dividedbyVstimes ^9?
44
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Mind-Bending Puzzles I
77.
When the proper weights are assigned, this mobile isperfectly balanced.Can you determine the three missing weights?
(Hint:Try starting with the 8-foot sectionofthe mobile. Remember
that Distance Weight = Distance Weight.)
Ceiling
78.
Below are two numbers represented byxand y. Regardlessofthe values
ofxandy,allpossible answers resulting from the difference inthese two
numbers share one unique characteristic. What is it?
xy
- y *? ?
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Mind -Bending Puzzles I
79.
The perimeter of asquare hasavalue that is two-thirds ofthe number
representing itssquare footage.What is the sizeofthe square?
80.Find the hidden phraseortitle.
F R A M E
VIOLETVIOLETVIOLET
VIOLET
VIOLET
G A M E
46
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Mind-Bending Puzzles I
81.Find the hidden phraseortitle.
82.
F R A M E
IG A M E
In the gameofcraps, what are the chances that you will beawinneron
your first roll by getting eithera 7 oranII?
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Mind -Bending Puzzles I
183.
Here's another four-letter "trickle-down" puzzle. Find the three missingwords, each with only one letter changed from the previous word,to
arriveatBARN.
MOOD
BARN
What isthe valueofT inthe following puzzle?
A + B = H
H + P = T
T + A = F
B+ P+ F = 30
A = 2
48
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Mind -Bending Puzzles I
85.
If five potatoes and six onions cost$1.22 andsix potatoes and five onionscost $1.31, what does an onion cost?
86.Find the hidden phraseortitle.
49
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Mind-Bending Puzzles I
87.
Below are 10 matchsticksofequal length. By moving2and only2match-sticks, can you create2squares only, withnoleftover matchsticks?
88.You've been given $100 and toldtobuy 100 candlesfor aparty.The first
typeof candle costs $0.50, the second $5.50, and the third $9.50.You must
purchase exactly 100 candles and spend exactly $100. There is just one
solution. How many candlesofeach type are purchased?
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Mind-Bending Puzzles I
89.
Find the hidden phraseortitle.
90.Find the missing number inthe following series:
V12 '/ 3 '/ 4 '/ 6 '/12
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Mind -Bending Puzzles I
91.
Given the initial lettersofthe missing words, complete this sentence:
There are 206 B intheH B.
92.
What is the first number having factors that add uptomore than the
number itself? (Don't include the number itself as oneofthe factors.)
52
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Mind-Bending Puzzles I
193.
Find the hidden phraseortitle.
94.
One hundred people are applying forasales position that would require
themto sell both golf equipment and athletic shoes.Thirteen ofthe appli-
cants havenoprior experience insales. Sixty-fiveofthe applicants have
previously sold golf equipment, and78 ofthe applicants have sold athletic
shoes. How manyof the applicants have experience inselling both golf
equipment and athletic shoes?
53
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Mind -Bending Puzzles I
95.
Find the four-letter word that will make new words when added infrontof these:
GUARD
LONG
TIME
96.
What number is'/4of Vi of 'A of432, dividedby Vi ?
54
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Mind-Bending Puzzles I
97.
Find the hidden phraseortitle.
98.
What is the first year after the year 2000 inwhich the numbers of the
year will read the same right-side-up and upside-down? What is the second
year in which this will occur? (No fair using digital numerals, like2! )
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Mind -Bending Puzzles I
99.
What's the difference between I I yards square and I Isquare yards?
100.Find the hidden phraseortitle.
56
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Mind-Bending Puzzles I
1 0 1 .
A "perfect" number is anumber whose factors add upto the number (not
including the number itself). For example:
The factorsof 6are 3,2, and I and3 + 2 + 1 = 6 .
The factorsof28 are 14,7 ,4 ,2 , and I and 14 + 7 + 4 + 2 + I = 28.
What are the next two perfect numbers?
102.
H istoone asC istosix asN isto ?
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Mind -Bending Puzzles I
103.
What are the chancesofflippingapenny four times and gettingatleasttwo tails?
104.Find the hidden phraseortitle.
58
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Mind-Bending Puzzles I
105.
Decipher the following cryptogram. Each letter represents another letter
in the alphabet.
O T D X G A C O T ST B P W F W A S F T O O X .
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Mind -Bending Puzzles I
107.Find the hidden phraseortitle.
108.How many times in a 12-hour period are the handsofa clock directly
opposite each other?
60
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Mind-Bending Puzzles I
109.
A pipe can fillaswimming pool inthree hours.A second pipe can fill the
pool intwo hours.Ifboth pipes are turnedon at the same time, how long
will ittake themtofill the pool?
I 1 0 .
I am ten years older than my sister. There wasatime when Iwas three
times older than she was, andinone year Iwill be twice as old as sheis.
What ismy age now?
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Mind-Bending Puzzles I
I I I .
Find the hidden phraseortitle.
F R A M E
I IG A M E
I 1 2 .
Here's an interesting twist on an old series puzzle. Seeifyou can come
up with the missing letter. (Hint:This problem isbest approached with
an even hand.)
T F S E T T F ?
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Mind-Bending Puzzles I
113.
Twoofthe following statements are false.What are the real namesofeach
person?
Susie's last name isBillingsley.
Susie's last name is Jenkins.
Sally's last name is Jenkins.
1 4 .I
If you find the correct starting point in the wheel below and move either
clockwiseorcounterclockwise, the letters will spell outacommon every-
day word.What is the missing letter, and what is the word?
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Mind -Bending Puzzles I
1 1 5 .
Below, on the left,isalist of words, some of which may be unfamiliar. On the right
isalistofrelated, familiar words. Match the words in the second list to those in
the first.Take each word on the left and look for the related words you know for
sure.Then think of words that are similar to the ones you don't knowfor
instance,"potent" is like "potentate"and then look for a reasonable match!
1. gambol 6. ornithology 1 1. bovine a. tu rt le f. smell k. frolic
2. fortissimo 7. odori ferous 12. antipodes b. hats g. refined 1. raid
3. sort ie 8. gustatory 13. equivocal c. loud h. opposites m. soil
4. millinery 9. humus 14. potentate d. power i. cooking n. birds
5. culinary 10. terrapin 15.urbane e. ambiguous j. cow o.taste
I 1 6 .
Find the hidden phraseortitle.
64
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Mind-Bending Puzzles I
1 1 7 .
How many digits must be changed in the following addition problem tomake the sum equal 245?
89
16
+ 98
I 1 8 .
In a certain box of candy, the number of caramels is 25 percent of the
number of other candies in the box.What percentage are the caramels of
the entire box?
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Mind-Bending Puzzles I
I19.
Given the initial lettersof the missing words, complete the followingsentence. (Hint:Thinkofhydrogen.)
There are 106E inthePT.
120.Find the hidden phraseortitle.
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Mind-Bending Puzzles I
I
Ten men and8women can shovel as much snow in12 days as8men and
12 women can shovel in 10 days. Who are the better workers, menor
women, andbyhow much?
1 2 1
122.Change one and only one letter ineach successive word tocome up with
the next word:
ROAD
LOOP
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i
M i n d - B e n d i n g P u z z l e s I
123.
One of the following diagrams doesn't fit with the others. Which one isit?Why?
Here's fun with roman numerals. See if you can match column A to
column B.
V 100
M 500
C 1,000
C 5,000
L 10,000
X 50,000
D 100,000
D 500,000
M 1,000,000
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Mind-Bending Puzzles I
125.
Find the hidden phraseortitle.
F R A M E
V
AFFAIR
/WWW
G A M E
126.Using only the top rowofletters onatypewriter, what is the only
10-letter word that canbe created? Remember, the lettersare
Q W ER T Y U I O P
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Mind-Bending Puzzles I
127.
Inacertain game, a ball can fall through anyof 50 holes evenly spacedaroundawheel.The chance thataball would fall into any one particular
hole is I in50.What are the chances that2balls circling the wheelatthe
same time would fall into the same hole?
1 2 8 .
Find the hidden phraseortitle.
F R A M E
I ILQ 1Q ^ B- lb.
A M E
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Mind-Bending Puzzles I
129.
What is the missing number in the following series?
84 12 2 2/s '/io ?
I30*
Find the hidden phraseortitle.
^ A M -E
I GUILTY J[ o a m e
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Mind-Bending Puzzles I
131.
A man spent three-fourths ofhis money and then lost three-fourths oftheremainder.Hehas$6left. How much money didhestart with?
132.
Ina foreign language,"rota mena lapy" means large apple tree,"rota firg"
means small apple, and "mena mola" means large pineapple. Which word
means tree?
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Mind -Bending Puzzles I
133.
Unscramble the following word: O M A H G O L R
134.Seeifyou can determinearelationship among the following circlestofind
the missing number in the last circle.
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Mind-Bending Puzzles I
135.
Find the hidden phraseortitle.
136.
What isthe missing number inthe following series? (Hint: Could the num-
bers represent something other than quantities?)
13 9 14 4 - 2 5 14 4 9 14 ?
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Mind-Bending Puzzles I
137.
Molly and Maggie are Martha's mother's son's wife's daughters. Whatis Marthato Molly and Maggie?
138.
What familiar four-letter word canbeplaced infrontofeachofthe
followingto form four new words?
Shelf
Worm
Mobile
Mark
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M i n d - B e n d i n g P u z z l e s I
139.
In a shuffled deck of 52 playing cards, you alone are picking the cards outof the deck, and the cards are face down. What are the odds of your draw-
ing the Ace, King, Queen, and Jack of spades in succession:
I chance in 208?
I chance in 2,704?
I chance in 6,497,400?
I chance in 7,311,616?
I chance in 1,000,000,000?
140.
Given the initial letters of the missing words, complete this sentence:
There are 180 D in a T.
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Mind-Bending Puzzles I
141.
Below isateeter-totter witha 10-pound weight placed 10 feetto the left
of the fulcrum and an 8-pound weight placed5feetto the left of the ful-
crum. On the right sideofthe fulcrum is a 14-pound weight that needsto
be placedinorder tobalance the weights on the left side. How many feet
from the fulcrum should the 14-pound weight be placed?
10lb. 8lb. ^ 14
5ft.Fulcrum
10 ft.
142.How many different squares (of any size) are inthis figure?
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Mind-Bending Puzzles I
143.
Decipher the following cryptogram:
SALTS LA ELLG
144.
Find the hidden phraseortitle.
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Mind -Bending Puzzles I
145.
Use four movestoget from the first word tothe last.
BIKE
MATH
146.
The blankatthe bottomofthe second column below could be filled in by
any oneofthree words.What are these words?
EVIL POST
LIVE STOP
VILE TOPS
VEIL
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Mind-Bending Puzzles I
147.
Here'sa series problem that may requirea little extra patience.
3 I I 20 27 29 23 ?
148.
Unscramble this word: A T T R E S P N A R N
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Mind -Bending Puzzles I
149.
Find the hidden phraseortitle.
F R A M E
DIRTY DIRTY
DIRTY DIRTY
DIRTY DIRTY
DIRTY DIRTY
DIRTY DIRTY
DIRTY DIRTY
1 5 0 .
A squash tournament hassixroundsofsingle eliminationforits singles
competition.This includes the championship match, and there arenobyes.
How many players are entered when play begins?
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Mind-Bending Puzzles I A N S W E R S
1. There were20nickels and 20 dimes.To solve this,
set up the following equations, wheren=nickels and
d = dimes:
n=d
.05n +AQd =3.00
.05n+ .I0w= 3.00
.I5w =3.00
n =20
2.x=5,y=6, andz =4, so the sumis15.The vari-
able xcan be either0 or5.Itmust be5because
thereisno number that endsin 0when multipliedby
7(y 7, resultinginx).Therefore,a3 iscarried overto
they.Sincexis5,ymust be6because76 =42.
Add the3that was carried over and you get 45.
Therefore,zis4.
3. Itmight be helpfultoset up a grid as follows:
basketball football baseball
AlexRyanSteven
X o
o
X o x
X=Does not like
O =Likes
We can see that Ryan must like basketball since nei-
ther Alex nor Steven does. Steven does not like bas-
ketballorbaseball, so he must like football, leaving Alex
liking baseball.
4 . Look before you leap.
5.The missing number is lO.The numbers ineachcir-
cle add up to 50.
6.Seven zips have the weightof I wob.The problem
can be set up as follows:
26 z =4c+2w
8 z + 2c =1w
Rearranging, we get
(1) 26z = 4c+1w
(2) 8 z = -2 c +2w
Multiply equation (2) by 2 so that the c factor drops out,
and combine the two equations:
26 z = 4c+1w
16z = - 4c +4w
42 z = 6w
Iz= w
8.The next letter is R The differences between let-ters form the pattern 1,2,1,2,1,2...
9 .The answer is 96. Set up the following equations:
J_ 2 3
2 ' 3' 5 30
240 = 48
=96
IO. Figure4 is the only one that doesn't containa
triangle.
I I. Itis impossibletoaverage 60 miles per hour for
this trip. At 30 miles per hour, the car would travel one
mile in two minutes; at 60 miles per hour, the car
would travel two miles in two minutes. So, in orderto
average60 mph.the entire trip of two miles would
havetobe completed in two minutes. But the driver
has already used two minutes going from pointA to
pointB;there's no time lefttoget from point Bto
pointC.
12. The lesser of two evils.
13. Five.
14. The answer is "three words."
I5 .6.25 percent. Remember, length width=area.
Let/ = length andw- width. Then
/ + .25/ = 1.25/
w-.2Su> =.75w1.25/ .75w = 93.75
Finally,
100- 93.75 = 6.25
16. The chances are I in3. Here are all the possible
draws (CI =first cherry gumdrop, C2=second cherry
gumdrop,O =orange gumdrop):
First draw Second draw
CICIC2
C2
OO
C2OCIOCIC2
7. It's the right thingtodo.
Among the six possible draws, O appears twice in the sec-
ond drawcolumn;thus the chances are 2 in6,or Iin3.
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I7 .Here's one waytosolve the puzzle:
TOOKBOOKBOONBORNBURN
18. Time slips into the future.
19. There are 100 yearsina century.
2 0 . Letx=the fraction.Then:
4X " 12
2 7 .They can be combinedin12 different ways.
2 1 . Two miles.They are actually eating up the distance
at 120 miles per hour (50+70):
120 miles
60 minutes= two milesinone minute
2 2 .The "R" goes above the line.The letters above the
line are closed withaspace inside them.
2 3 . Pocket fullofmoney.
2 4 .The letters "mot" will create the words "mother"
"motion," "motor," "motif," and "motto."
2 5 . .1 .9 .8=.072
2 6 .The answeris(e). Remembei;xmay be a negative
number
11
2 8 . Line dance
2 9 . He would have 20 pleezorns. Count the lettersin
each name and multiply by2.
30 .The ratiois I to2. One waytosolve this prob-lem istoset up an equation in whichxequals the
amountof$48 chemical used andyequals the
amount of $36 chemical used:
48x + 36y= 40(x +y)
48x+36j>= 40x+40j*
8x =4y
_x
y
3I .Traffic jam
32 .There are 31 triangles.
3 3 . Don't count your chickens before they hatch.
3 4 .The ratiois I to2.Itmight helptoset up the
problem as follows:
5x_ 7_
~ 8
40x = 28y
IOx = ly
Thus, I 0x t o7 j ' i sa l- to -l relationship.We are asked
for the ratioof IOx to 14y\ since 14= 7 2, we can
see that itisa l-to-2 relationship.
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3 5. J J.The letters are the initial lettersofpairsof
month names, starting with October-November:
3 6 .Three-ring circus
3 7. Here are 20 four-letter words:
twin wine lintkiln kilt lentwink wilt likelink welt kine
tine tile lien
newt kite line
went wile
3 8 . The missing numbers are 18 and 5, respectively.
There are actually two separate seriesofnumbersin
this puzzle. Look at every other number; beginning first
with8and then with15.
39.The answer is I3,222.
I 2,000+1,222
I 3,222
4 0 . Forward thinking
4 1 . !/24.
2. _ J_=J_32 16 " 32
4 2 . Draw a line as follows and you'll see the answer;June:
*4 3 . Double-decker sandwich
4 4 . In the first case, 267 islarger In the second case,
they are equal.
4 5 . Microorganism
4 6 .There isone wheelon aunicycle.
4 8 . Here they are:
= 6,729
2 13,458
J_ = 5,832
3 17,496
J_ = 4,392
4 17,568
J_ _ 2,769
5 13,845
J_ _ 2,943
6 17,658
= 2,394
7 16,758
J_ _ 3,1878 25,496
= 6,381
9 57,429
4 9 . ibeforeeexcept after c
5 0 . The valueofzmust be9 inall cases.
5I .The valueofxis I.The variableycan have anyof
a numberofvalues, butxmust always equal Iandz
must always equal9.
5 2 .Yes.Anumber is divisible by8 ifits last three dig-
its are divisible by 8. Examples: 6,240;9184; I5,536.
53 . Doorbell. All the rest have handles.
54 . FigureCis the only figure without a straight line.
5 5 . Right cross followed by an uppercut.
56 . For these three numbers, 455 is the lowest com-
mon denominator
57 .Youwould write it17 times. Don't forget that
there are two 4sin44!
5 8 . Fillinthe blanks.
4 7 . Fifteen angles oflessthan 90 degrees can be formed.
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Mind-Bending Puzzles I A N S W E R S
59 . 107 percentof300 is greater. Because 107 per-
cent is equivalentto 1.07, we have
1.07 300
.50 600
321
300
60.The answer is l0/33. The problem can be solved
as follows:
I I I
3+- 3+- 3+-10
33
10
133
61.1 8 13 12
14 1 1 2 74 5 16 9
15 10 3 6
6 2 .Test patterns
6 3 . Here's one way:
6 4 .Youwould receive 221 silver pieces. Ifyouwereto
exchange your kooklas only for gold,itwould require
40 7 or280 pieces. But there are only I 61gold
pieces, leaving you I19 gold pieces short.The valueof
silver coinstogold coinsisin the ratioof I 3to 7:
13 _ X7 ~ M9
1X =1,547
X =221
6 5 .The missing number is 35.The second numberin
each box is the square of the first number minus I.
66.There are 720 possible arrangements. Use the fol-
lowing equationtosolve the problem (this is called
factorial notation):
6!= 654 3 2 I =720
6 7 . Hole inone
68.Algebra
6 9 .The number 9 goes below the line and the num-
ber 10 goes above itthe numbers 1,2, 6, and 10 are
all spelled with three letters; the rest have fourormore.
7 0 .Your eyes are bigger than your stomach.
7 1 . Here are two examples:
I .When giving yes and no answers, a person who tells
a lie about alieis telling the truth.
2. Imagine a child rolling his wagon backward downa
hill. If you weretofilm this and run the film backward,
you would see the wagon going forward up the hill.
72.
73 .There are 24 cubes.
7 4 .They sayatleast 100 words canbemade from
"Thanksgiving." How many can you find?
7 5 . Elbow grease
7 6 . It is7/9.The problem canbeapproachedas
follows:
I I10 - ! 210
I =9 9
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M i n d - B e n d i n g P uz z l es I A N S W E R S
7 7 . x,y,andz= 8, 12, and 60 pounds, respectively.
Starting with the 8 ft. section,
8 ft. - 10 lbs. = 80 ft.-lbs.
To balance, the bottom left part of the mobile must
also equal 80 ft.-lbs., so its total weight must be 20 lbs.
(4 ft.20 lbs. = 80 ft.-lbs.) Therefore,x+y = 20
and
6x = 4ji
So,
y =20 -x
and substituting,
6x = 4 (20 -x)
6x = 80 - 4x
IOx = 80
x = 8and therefore,y = 12
Adding the total weights of the left side, we have
12 0+ 10 + 8 + 12 = 150 lbs.
150 lbs. 4 ft. = 600 ft.-lbs.
Therefore, the right side must also be 600 ft.-lbs.:
IOft.ri bs . = 600 ft. lbs.
2- = 60
7 8 .All answers are divisible by three.
79 .The square is 6 feet by 6 feet.To solve this prob-
lem, letx represent each side of the square.Then
24x =x1-
\2x= 2x 2
6x =x1
x 6
8 0 . Shrinking violets
8 1 . Calm before the storm
8 2 . 2 in 9. Because each die has 6 faces, there are
6 6 or 36 possible combinations of numbers. Of
these, 6 combinations result in a 7:
6 and I
1 and 65 and 2
2 and 54 and 33 and 4
And 2 combinations result in an I I:
5 and 66 and 5
thus the chances are 8 in 36, or 2 in 9.
83.
MOOD
MOON
MORNBORN
BARN
8 4 .T = 15. Since A = 2, we can substitute A into the
first four equations to come up with the following:
(1) 2 + B = H
(2) H + P = T
(3) T + 2 = F
(4) B + P + F = 30
Now substitute equation (I) into equation (2):
(2+ B) +P = J
Rearranging, we get
B + P = T - 2
Substitute this into equation (4):
(T - 2) + F = 30
Finally, substitute equation (3) into equation (4) and
solve forT:
(T - 2) + (T + 2) = 30
2T = 30
T = 15
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Mind-Bending Puzzles I A N S W E R S
8 5 .An onion costs7cents. Set up the equations,
withxasapples andyas onions:
5x + 6y
6x +5y
1.22
1.31
Multiply the first equationby6, the second oneby 5:
30x+ 3 6 y - 7.3230x+ 25y=6.55
Subtract the second equation from the first, and you
have:
Ox + IIy= 11
'y= -07
86.Rising tide
8 7 . Itcan be done as follows:
I 10
88.Let's havex,yandzrepresentthree types of candles.
x+y+z =100and
,50x+ 5.50j>+9.50z = $100
Multiply the first equation by -.5, and combine itwith
the second equation:
- 5 x -5y- 5z= - 50
5x+5.5^+ 9.5 r = 100
5_y +9z - 50
5y=50 -9 r
y =
Since we're dealing with whole numbers, zmust beawhole number andamultipleof5. In this case zcan
only equal 5.With any greater number,ywill become
negative, soz=5,y= I, and thusxmust be 94.
(94 .50)+ (I 5.50)+ (5 9.50)=$100.
0
8 9 . Multiplication tables
9 0 .The missing number is zero.Ifyou convert each
fractiontotwelfths, you get the following series:
A A 2 A _L12 12 12 12 12
9 1 . There are 206 bones in the human body.
9 2 . Factors ofthe number 12(6+ 4 + 3 +2+ I)add
upto16.
9 3 . Deep in thought
9 4 . Fifty-six applicants have experience inselling both
golf equipment and athletic shoes. Since 13 of the
applicants have hadnosales experience, we're dealing
with87people who have some experience. Of the87
applicants, 65 of them have sold golf equipment, whichmeans that22of this group haven't sold golf equip-
ment (87- 65=22). Seventy-eight of the applicants
have sold shoes, which means that9haven't (87- 78
= 9).Therefore, we have9 +22or3I people who
could not have sold boththus, 87- 3I= 5 6people
who havehad experience inselling both.
9 5 . Life
9 6 . 18. '/4of '/3of '/6is '/72; {/72of 432 is 6;
and6dividedbyV3is 18.
9 7 .You are on time.
9 8 . 6009, 6119
9 9 . I10 squareyards.An area I Iyards square meas-
ures I Iyards on each of four sides and therefore has
a totalof121 square yards.An areaof I Isquare
yards,if itwere square, would be just under 3.32 yards
on each side.The difference between the two, then,is
found by subtracting I Isquare yards from 121 square
yards: I10 square yards.
100. Can't see the forest for the trees
I O I .They are 496 and8,128. The next perfect num-
ber after that is 33,550, 336!
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Mind-Bending Puzzles I A N S W E R S
102. Seven.These are the elements hydrogen, car-
bon, and nitrogen with their respective atomic num-
bers; seven is the atomic number for nitrogen.
103.There are 16 possibilities, each havingaprob-
abilityof '/i 6.There are6ways with exactly2tails,
4 ways with 3tails, and I way with4tails.That'sa
totalof I Iways outof16.The chances are II in 16.
HHHH TTTT
HTTT THHH
HHHT TTTH
HTHH THTT
HHTH TTHT
HHTT TTHH
HTHT THTH
HTTH THHT
104 .Abreak in the action
105. Let a smile be your umbrella.
106.
108.They are directly opposite each other I Itimes.
109. Itwill take 1.2 hours.
The equation can be set up this way:
T +T " '
Multiply by6:
2x+ 3x = 6
5x = 6
I 10. Iam 19 years old and my sister is9.
Letx =my sister's age andy -my age.
y=x+ 10 and
y+ I=2(x + I)
y=2x+\
Substituting this result inour first equation,we have
2x+ I = x+ 10
x= 9
so
y = 19.
When my sister was 5, I was 3 times older than she was.
I I I . Look both ways before crossing.
I I2.The missing letter is S.These are the first lettersof
the even numbers when spelled out, beginning with two.
113. Sally Billingsley and Susie Jenkins are the real
names. Because one of the first two statements hadto
be false, the third statement also hadtobe false.
I 14. The missing letter is N;the word is "sandwich."
115.1. gambol k. frolic
2. fortissimo c. loud
3. sortie 1. raid
4. millinery b. hats5. culinary i. cooking
6. ornithology n. birds
7. odoriferous f. smell
8. gustatory 0. taste9. humus m. soil
10. terrapin a. turtle
1 1.bovine cow12. antipodes h. opposites13. equivocal e. ambiguous
14. potentate d. power
15. urbane g- refined
116. Power surge
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Mind-Bending Puzzles I A N S W E R S
I I 7 .None, Instead, turnthepuzzle upside-down
and add:
86
91
+ 68
245
I 18.20 percent. Say there are 10 caramels. Since thenumberofcaramelsis25 percent of the numberof
other candies, there must be 40 piecesofcandy that
aren't caramels.The total numberof piecesofcandy=
10+40=50, sol0/50= 'A =20percent.
I 19. There are 106 elements in the periodic table.
120. Fender bender
121. Women are the better workers. Let's say thatin
one day, 10 men workata rateof xand8women
workata rate ofy.
IOx +8y =j y (one day), or 120x + 96_y= I
Likewise, in the second case:
8x+ 12y= ,or80x+ 120y= I.
Therefore:
120x+96_y=80x+ I20>>
5x = 3y
Thus, 3 women do the workof5men.
I 22 . Here's one waytosolve the puzzle:
ROADROAMROOMLOOMLOOP
123. Diagram E is the odd one out The other four
are symmetrical about both of their axes:ifyou turn
them 90 degrees, they will look the same as in their
original positions.
C = 100
D = 500
M = 1,000
V = 5,000
X = 10,000
L = 50,000
C = 100,000
D == 500,000
M =: 1,000,000
125. Current affair
126.The word "typewriter" is the only word that can
be created.
I 27 .The chances are still I in 50.
I 28 .Central Intelligence Agency
129.The missing number is '/3o.The seriesiscon-structed as follows:
12 = Vl of 84
2 = '/6o f12
2/s = '/5 of2
'/io = '/4Of2/5
'/30 = '/3 of'/io
I 30. Guilty beyondareasonable doubt
131. $96. Use the equation
*-(J-. i -*)= $6
Multiply each sidebyI6:
4 x - 3x = $96
x = $96
I 32. "Lapy" means tree. From the first two phrases,
"rota" must mean apple. From the third phrase,
"mena" must mean large, leaving "lapy" to be tree.
133. Hologram
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Mind-Bending Puzzles I A N S W E R S
I 34.The numbers ineach circle add upto 150, so
the missing number is 23.
135. No time left on the clock
I 36. The missing number is 7,The numbers havea
one-to-one correspondence with the letters of thealphabet, whereA = I,B=2,C =3, and so forth.The
word spelled out is "mind-bending."
I 37. She is their aunt
I 38. Book
I 39.The chanceofdrawing the aceofspadesis I in
52; for the king,I in5 I; for the queen, I in50; andfor
the jack, I in49.To calculate the answer; multiply these
altogether:
'/52X !/51X '/50x '/49 = 1/6,497,400
140.There are 180 degreesina triangle.
141 . The weight should be placed 10 feet from the
fulcrum.To solve this, first calculate foot-pounds (a unit
of work combining force and distance) on the left side:
(5 ft.-8lb.)+(10 ft.-10 lb.)= 140 ft. lb.
The right side must equal the left side:
xft. 14 lb.= 140 ft. lb.
Solving forx,we get
146. POTS, SPOT, and OPTS.These are the only
three remaining four-letter words that can be madeby
using the letters O,R S,andT only once.
147.The missing number is 6. Keep taking the differ-
ences between numbers (keeping in mind positive and
negative differences) and you get:
3 I I 20 27 29 23 6
v v v v v /8 9 7 2 - 6 -1 7
W W /I -2 -S -8 -II
v w /- 3 -3 -3 -3
148.Transparent
149. Dirty dozen
I 50. With players for each match through six rounds,
26or64 players are entered.
142.There are 19 squares.
143. Knock on wood.
144. Slim chance
145.
BIKE
BITEMITE
MATE
MATH
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M i n d - B e n d i n g P uz zl es I S C R I B B L E P A G E
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M i n d - e n d i n g P n i l e ? I
by ^e rc y S t ick e is
This ec lect i: co lf ^C ion of 150 puzzl ;s wm .ave yor Do .i .eling wh b S'. sfecti n id
scratch ing yc ur I >ac! pc>le;ity as - ou w r r K ou t sc1, ti< is.-From math, word,
a n i fogic problems to v -ua l riiagn rr.s a 1 Fr . rh*1G ; est-hi challengi ng stampers;
wi l1 provid e hours c activ ity fo r ill p i :zle fienas //ho find nentai aerobu t o be the
best wa to stay in shape!
A u A o r T e r v Sticker i; contributing wri ter f, Discove , nd Games agz ines and
conducts business anc educational semi jars on cri tical Kinking skills. We re's what tha
ritics say abGuti is puzzles:
Terry Stickeis's puzzle collections are highly recommenced fGi their noveapproaches and fresh ideis.
Mart in Gardner, wr i te r and forme editor of
Scientific American's muzzle co iu .nn
Terry Stickels's puzzles are fresh, varied, and well thought outand the) luiici
problem-solving skills that are useful both academically and in evei yday life,
W i i l Shor tz , crossword ed .tor ,The New YorkTimes
[Terry Stickeis offers] a fresh approach to problem solving and bramteasers.
The Mathematics Teacher
Don't liss Mind-Bending Puzzles,volumt II and T e r r ' Stickels's Mind-Bending Pi zzies
calendar rn d decks of Knowl edge lards, i ll ublis hrd b Pomegranate,