GREATCRITICAL THINKINGPUZZLESMichael A. DiSpezio

       GREAT

 CRITICAL THINKING

. PUZZLES

Michael A. DiSpezio

mustrated hy Myron Miller

II

Sterling Publishing Co., Inc. New York

Library of

Congress Cataloging-in-Publication Data

Dispezio, Michael

A.

Great critical thinking puzzles / by Michael

illustrated by Myron Miller.

p. cm.

Includes index.

ISBN 0-8069-9725-7

1. Puzzles. 2. Critical thinking.

II. Title.

GV1493.D557 1997

793.73-dc20

A. DiSpezio ;I. Miller, Myron, 1948- .

1 3 5 7 9 10 8 6 4 2

Published by Sterling Publishing Company, Inc.

387 Park Avenue South, New York, N.Y. 10016

©

Distributed in Canada by Sterling Publishing

96-46532

CIP

c/o Canadian Manda Group, One Atlantic Avenue, Suite 105

Toronto, Ontario, Canada M6K 3E7

Distributed in Great Britain and Europe by Cassell PLC

Wellington House, 125 Strand, London WC2R OBB, England

Distributed in Australia by Capricorn Link (Australia) Pty Ltd.

P.O. Box 6651, Baulkham Hills, Business Centre, NSW 2153,

Australia

1997 by Michael A. DiSpezio

Manufactured in the United States of America

All rights reserved

Sterling ISBN 0-8069-9725-7

CONTENTS

•••

Introduction

5

The Puzzles

7

The Answers

65

Index

95

Acknowledgtllents

Very few things are produced (or solved) in a vacuum.

It is through the nurture, encouragement, playfulness,

and caring of others that books such as

Critical Thinking Puzzles

With sincere gratitude, I appreciate the support

and value that my family placed on education.

Through the opportunities made available, I was (and

am) able to purse my interests in creativity, teaching,

performance, and science. Along the way, many individuals

knowingly (and unknowingly) helped finetune

my path. These people are friends and colleagues

whose talents, skills, and capabilities have had

a noted effect. They include Norman Levin, David

Franz, William

Gascoyne, Edward O'Toole, ] onathan Elkus, ] onathan

Larkin, Bob Higgins, Stewart (Buzzy) Hirsch, Karen

Ostlund, Shirley Watt Ireton, Jocelyn Lofstrom, Bob

Hall, Mike Kane, Warren Stone, Genie Stevens, Paul

Mascott, Dennis Colella, Thomas Lineaweaver, Brian

Shortsleeve, Doug Horton, my dedicated editor

Hazel Chan, Myron Miller for his cartooning genius

and puzzle-solving aptitude, and my friends, colleagues,

and "extended family" in the Middle East

and on Wilson Boulevard (NSTA).

Closer to home, I'd like to thank my son, Anthony,

for being the best puzzle tester I've ever met.

Greatare created.Harri~, Ken Read, Steve Golubic, Peter

4

INTRODUCTION

Hang on to your brains because here we go again!

In

this follow-up adventure to Critical Thinking

Puzzles,

your critical thinking skills. From mental paths

to army ants, you'll encounter an assortment of challenges

that are designed to pump up your brain

power.

Psychologists and educators refer to critical thinking

skills as a variety of higher-level thinking strategies

that can be used to analyze, solve, and evaluate

all sorts of things, such as facts, theories, statements,

and, of course, puzzles. The array of brain-bending

puzzles presented in this book should engage many

of these skills.

You will have to uncover assumptions, solve by

analogy, sequence events, generalize, and discover all

sorts of patterns. You will also find yourself digging

deeper into your brain to come up with some creative

possibilities. Once generated, novel possibilities need

to be analyzed in order to determine if they work.

I present more of the best puzzles for stimulating

As

with a new twist. For centuries, they have challenged

and entertained people. But unbeknownst to

the puzzled, these conundrums were also producing

new thought channels that had been etched into the

cells, chemicals, and electrical patterns of the brain.

Most of the puzzles here can be done with a pencil

or pen. Others require simple items, such as loose

in my first book, there are old-time favorite puzzles

5

change or matchsticks, that can be found around the

house. But what they all need is for you to be creative

and inventive in solving them.

So why wait? Just jump right in and you will be on

your way to boosting your critical thinking skills

again!

-Michael

6

--.-------~-,

THE PUZZLES

Brain Net

•••

Your brain is an incredible piece of machinery. About

the size of a squished softball,

brain cells. These cells make more connections than

all of the phones in the world. It's this huge network

that produces your brain power! Want to feel the

"brain net" in action?

Take a look at the drawing below. Your job is to figure

out how many different paths can get you across

from start to finish.

You can only move to the right. You can't go back.

When you arrive at a "fork," take either the top or

bottom route. Start counting.

it contains billions of

Answer on page 66.

8

Predicting Paths

......

One of your brain's most powerful capabilities is the

ability to think visually. When we think in this way, we

construct a mind's eye image of a shape, scene, or

concept. This image can be rotated, changed, moved,

and analyzed. How good are you at visual thinking?

Here's your first chance to find out.

Suppose we roll the wheel along the flat surface.

Draw the shape that would be traced by the point

within the wheel.

o

Now let's put the small wheel along the inner rim

of a larger circle. What shape path would a point on

the smaller wheel trace?

9

Finally, suppose the inner wheel remains stationary.

What pattern would be traced out by a point on the

larger rim as it rolls around (and remains in contact

with) the inner wheel?

Answers on pages 66-67.

Who's That?

•••

Look into a mirror and who do you see? You?

Perhaps, but it's not the same you that everyone else

sees. Its a right-left reversed image. The ear that

appears on your left side is seen by others on your

right side.

Suppose you want to see yourself exactly as others

see you. How can you set up two small mirrors so that

your reflection isn't reversed?

Answer on page 67.

10

Leftovers Again?

•• +

Your brain is divided into two halves. The left half is

more number-oriented, rational, and concrete. Your

right half is more creative, playful, and artistic. To

solve this next puzzle, you'll have to borrow a little

from both sides of your brain.

In an art class, students are taught how to shape a 1

ounce bag of clay into a small statue. During this

process, some clay remains unused (actually, it falls to

the floor). For every five statues that are made, there

is enough extra clay to make one more statue.

Suppose a student is presentedwith 25 ounces of clay.

What is the maximum number of statues he can

sculpt?

'*'~

left 6~S\IN's ~T'\'.LA~lE£f.

COULtl~'r

I JUST 1>0 ONt

~l(; OH~?

r--~==-

Answer on pages 67-68.

11

Brownie Cut

......

Now that art class is over, it's time for cooking class.

A chocolate brownie emerges from the oven. Karen

cuts the square brownie in half. She then divides one

of the halves into two smaller but equal parts.

Before she can eat the larger piece, two of her

friends unexpectedly arrive. Karen wants everyone to

have the same amount of dessert.

of cuts, how can she produce three equal portions?

In the fewest number

Answer on page 68.

12

Balan

.c.i.n.g Gold

A gold bar balances with nine-tenths of 1 pound and

nine-tenths of a similar gold bar. How much does

each gold bar weigh?

Answer on page 68.

Thrifty

Technique

•••

Don't put that balance away! You'll need it along with

a few pounds of brain cells to help solve this next

problem.

13

By the way, did you know that Albert Einstein's

brain was "normal" in weight? For the most part, it

resembled an ordinary brain. There was, however, a

slight difference. He had extra "cleanup" cells (called

neuroglial cells). These cells move around the brain

to get rid of dead or injured nerve cells. Perhaps his

"well swept" brain supercharged his intelligence?

You have nine gold coins. One of the coins is counterfeit

and is filled with a lighter-than-gold substance.

U sing a balance, what strategy can you use to uncover

the counterfeit coin?

To make things a little more difficult, you must

identify the fake coin with only two uses of the balance.

Answer on pages 68-69.

Tricky Tide

......

In the Bay of Fundy, the tides can vary in height by

almost 50 feet. The bay in our puzzle has a tidal

range of only 6 feet. A boat moors in the middle of

this bay. A ladder hangs down from the deck of the

boat and touches the flat sea surface. The rungs are 1

foot apart.

At low tide, ten rungs of the ladder are exposed. At

high tide, the water level rises 6 feet. How many of

the rungs will remain exposed?

Answer on page 69.

14

Breaking

Up Is

Hard to

Do

•••

How fast can you think? Faster than a speeding bullet?

Faster than electricity? For most of us, thoughts race

around our brains between 3 to 300 mph. Who knows,

this puzzle may break your brain's speed record.

The square encloses a 4 x 4 grid. There are five

different ways this grid can be divided into identical

quarters. Each way uses a different shape. Can you

uncover the layout of all five patterns?

Answer on page 69.

15

Disorder

+++

Buildings crumble. Living things decompose. It's a

scientific principle that things tend to go from order

to disorder. The fancy name for this principle is

entropy. There are, however, a few things that appear

to go against this tendency. Crystals grow and become

more complex. Living things take simple chemicals

and build complex tissues.

This puzzle, however, uses entropy. Notice how

neat and orderly the arrangement of numbers is.

Now, let's play the entropy game and rearrange the

numbers so that no two consecutive numbers touch

each other. They cannot align side by side, up and

down, or diagonally.

1

2

3 4

5 6

7

8

Answer on page 69.

16

True or False?

•••

Here's a totally different type of problem. This one is

based on logic.

Two cultures of aliens live on the planet Trekia, the

carpals and the tarsals. The carpals always lie. The

tarsals always tell the truth.

A space traveler arrives on Trekia and meets a

party of three aliens. She asks the aliens to which culture

they belong. The first one murmurs something

that is too soft to hear. The second replies, "It said it

was a carpal." The third says to the second, "You are a

liar!" From this information, figure out what culture

the third alien belongs to.

,

Answer on page 70.

17

Pack Up Your Troubles

•••

A fragile item is to be shipped in a cardboard box.

In

order to prevent the item from hitting against the

walls of the box, plastic foam cubes are used as

"bumpers." There are ten of these cubes. How can

you position them along the inner walls of the box so

that there is an equal number of cubes along each

wall?

dll

<1N3

__ ........I

SlflJ.

- .J

18

Answer on page 70.

Don't Come Back This

W"ay Again!

++.

The pitcher plant is a carnivorous plant that eats

insects.

plant's flower. When it tries to reverse direction, it

can't. Tiny spines on the petals' surface face downward,

which forces the insect to move in one direction-

down.

Here's your chance not to go back. The shape

below is made with one continuous line. Starting anywhere,

can you complete the shape without lifting

your pencil from the page? As you probably guessed,

your path cannot cross over itself.

An unfortunate insect walks into the pitcher

Answer on page 70.

19

Meet Me on the Edge

•••

Did you know that an ant can lift about fifty times its

body weight? If you had that power, you'd be able to

lift over 2 tons!

Suppose we position one of those powerful ants on

a corner of a sugar cube. On the opposite corner, we

position a fly. Suppose the two insects begin walking

towards each other. If they can only walk along the

edges of the cube (and never go backwards), what is

the probability that their paths will cross?

20

h.

AtJ~, No ""AlC~UfJ6- 0 tJ fHE ~,

SuGAR

CUSE "lo~c,. !lff WA'I- i ~Answer on page 71.http://www.sakshi.com/