Mind Bending Puzzles 1.pdf

7/25/2019 Mind Bending Puzzles 1.pdf

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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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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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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 .


12


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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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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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1 7 .

Try your luckatthis "trickle-down" puzzle. Startingatthe top, change oneletterofeach succeeding word toarriveatthe wordatthe bottom.

TOOK

BURN

1 8 .



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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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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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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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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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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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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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31.


32.

How many trianglesofany size are inthe figure below?


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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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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.


F R A M E

G A M E


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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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39.

Do this quickly: Write down twelve thousand twelve hundred twenty-two.

40.



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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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43.


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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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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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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49.


ISO.

What is the valueofz\r\ the following problem? (Each number isapositive

integer between0and9.)

y+z

xy


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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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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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55.


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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57.

If you wrote down all the numbers from5 to83, how many times would

you write the number 4?


F R A M E

BLANKfill

BLANKfill

BLANK

G A M E

35


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59.

Which is greater, 107 percentof300or 50percentof600?

60.What is the valueofthe following?

3 +3 ' / 3

36


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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


F R A M E

1"F3G A M - E


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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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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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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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69.

Do the numbers9and 10 go aboveorbelow the line?

3 4 5 7 8

70.


41


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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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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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75.


76.

What isV\odividedbyVi dividedbyVstimes ^9?

44


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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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79.

The perimeter of asquare hasavalue that is two-thirds ofthe number

representing itssquare footage.What is the sizeofthe square?


F R A M E

VIOLETVIOLETVIOLET

VIOLET

VIOLET

G A M E

46


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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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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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85.

If five potatoes and six onions cost$1.22 andsix potatoes and five onionscost $1.31, what does an onion cost?


49


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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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89.


90.Find the missing number inthe following series:

V12 '/ 3 '/ 4 '/ 6 '/12


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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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193.


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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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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97.


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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99.

What's the difference between I I yards square and I Isquare yards?


56


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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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103.

What are the chancesofflippingapenny four times and gettingatleasttwo tails?


58


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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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108.How many times in a 12-hour period are the handsofa clock directly

opposite each other?

60


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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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I I I .


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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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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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 .


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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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I19.

Given the initial lettersof the missing words, complete the followingsentence. (Hint:Thinkofhydrogen.)

There are 106E inthePT.



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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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125.


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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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 .


F R A M E

I ILQ 1Q ^ B- lb.

A M E

70


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129.

What is the missing number in the following series?

84 12 2 2/s '/io ?

I30*


^ A M -E

I GUILTY J[ o a m e


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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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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.

73


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135.


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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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.

76


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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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143.

Decipher the following cryptogram:

SALTS LA ELLG

144.



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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

79


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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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149.


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?

81


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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.


88/100


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.

86


89/100


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.


90/100


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

88


91/100

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


92/100


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!

90


93/100


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


94/100


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


95/100


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


96/100

94

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


97/100

M i n d - B e n d i n g P uz z le s I S C R I B B L E P A G E


98/100

M i n d - B e n d i n g P u zz le s I S C R I B B L E P A G E

96


99/100


100/100

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,

Mind Bending Puzzles 1.pdf

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