Only the Shadow Knows?
+++
A medium-size jet has a wingspan of 120 feet. An
albatross is a bird with a wingspan of about 12 feet. At
what altitude would each object have to fly in order to
cast shadows of equal size?
Answer on page 71.
More Shadow Stuff
+++
At a certain time of day, a 25-foot telephone pole
casts a 10-foot shadow. At that same time, how high
would a tree have to be
shadow?
i~ order to cast a 25-footAnswer on page 71.
Trip Times
+++
Did you know that the speed record for cars is over
700 miles per hour? To attain this supersonic speed,
the cars use rocket engines. They move so quickly
that if the car body had wings, the vehicle would fly!
The car in our problem is much slower. In 1 hour,
traveling at 30 mph, it climbs to the top of the hill.
'When the car reaches the top, the driver remembers
that she left her field guide to mountain life back
21
home. She immediately turns around and drives
downhill at 60 mph. Assuming that she spent no time
at the top, what was her average speed?
HINT: It is not 45 mph.
Answer on page 71.
Average Puzzle
•••
How fast can you ride a bicycle? To get into the
Guinness Book of Records
you'd need to ride faster than 60 mph.
An ordinary cyclist travels up and down a hill.
Going up, she maintains a constant speed of 10 mph.
It takes her 1 hour to get to the top. Assuming that
the hill is symmetric, what speed must she maintain
on the way going down if she wishes to average 20
mph? Before you bask in victory, the answer is not 30
mph.
for human-powered cycling,Answer on page 72.
Palindrome
•••
A palindrome is a word or number that reads the
same backwards as it does forward. Numbers such as
606 and 4334 are palindromes.
While driving his car, Bob (so much of a palindrome
lover that he changed his name from John to
22
Bob) observes that the odometer reading forms a
palindrome. It displays the mileage 13,931.
Bob keeps driving. Two hours later, he looks at the
odometer again and, to his surprise, it displays a different
palindrome!
What is the most likely speed that Bob is traveling?
Answer on page 72.
Stacking Up
++.
Can you arrange these numbered blocks into three
equal stacks so that the sum of the numbers displayed
in each stack must be equal to any other stack.
mIT]
ITJJGJJlTI
GJJ[TIJIT][!]
Answer on page 72.
23
Star Birth
•••
Trace this octagon pattern onto a separate sheet of
paper. Then decide how to divide this shape into
eight identical triangles that can be arranged into a
star. The star will have eight points and an octagonshaped
hole in its center. When you think you've
come up with an answer, trace the pattern onto the
octagon. Cut out the separate parts and reassemble
them into a star.
Answer on page
73.24
Flip Flop
+++
Did you know that the ancient Egyptians believed
that triangles had sacred qualities? This may have led
to the superstition about walking under a ladder.
~en
To walk through the triangle might provoke
the wrath of the gods.
The triangle below is made up of ten disks. Can
you move three of the disks to make the triangle
point in the opposite direction?
a ladder is placed against a wall, it forms a triangle.Answer on page
Crossing Hands
+++
Picture in your mind a clock with a face and hands.
Between the hours of 5
will the hour and minute hands cross each other?
AM and 5 PM, how many timesAnswer on page
25
What's Next?
•••
Examine the figures below. Can you see what the pattern
is and find out what the fourth figure in this
series should look like?
2
Answer on page 74.
26
Trying Triangles
+++
How many triangles can be found in this figure?
Answer on page 74.
Flipping Pairs
+++
Place three coins with their indicated side facing up
as shown. In three moves, arrange the coins so that
all three have the same side facing up. A move consists
of flipping
NOTE: Flipping the pair of outer coins three times
doesn't countl
two coins over to their opposite side.Answer on page 74.
27
Missing Blocks
•••
Examine the figure of blocks below. Let's assume that
the hidden blocks are all in place. How many additional
blocks are needed to fill in the empty region to
complete this cube?
Once you've made your guess, look at the pattern
again. Assume that the hidden blocks are all in place.
Now let's suppose that all of the blocks you can see
are vaporized. How many blocks would be left
behind?
Answers on page
28
Matchstick Memories
......Years ago, matchsticks were made from small sections
of wood. These common and inexpensive objects
were perfect props for after-dinner or parlor room
activities. Nowadays, toothpicks offer the same advantages.
So get your picks together and arrange them in
the three patterns shown below.
x
\/
As you can see, each line of matchsticks forms an
incorrect equation. The challenge is to make each
one correct by changing the position of only one of
the toothpicks in each row.
Answers on page 75.
29
Sum Circle
•••
Place the numbers one through six within the six
smaller circles shown below. Each number must be
used only once. The numbers must be placed so that
the sum of the four numbers that fall on a circle's circumference
is equal to the sum of the numbers on
any other circle's circumference.
Think it's easy? Give it a try.
Answer on page 75.
30
Many
Rivers to Cross+++
Let's take a break from puzzles and go on a rowboat
ride across the river. There are four adults who want
to cross it. They come upon a boy and a girl playing
in a rowboat. The boat can hold either two children
or one adult. Can the adults succeed in crossing the
river? If so, how?
Answer on page
76.31
Train Travel
•••
A train travels at a constant rate of speed.
stretch of track that has fifteen poles. The poles are
placed at an equal distance to each other.
train 10 minutes to travel from the first pole to the
tenth pole. How long will it take the train to reach the
fifteenth pole?
It reaches aIt takes the32
fl£ASE,
Relll\'s. CANW~
Go Ho M.~ tF VOl' OotJITftGVf£
tT 11IT TH1S 1R'P~t:O
Answer on page 76.
Miles Apart
•• +
The distance from New York to Boston is 220 miles.
Suppose a train leaves Boston for New York and travels
at 65 mph. One hour later, a train leaves New
York for Boston and travels at 55 mph.
the tracks are straight paths and the trains maintain a
constant speed, how far apart are the trains 1 hour
before they meet?
If we assumeAnswer on page 76.
Passing Trains
•• +
Coming from opposite directions, a freight train and
a passenger train pass each other on parallel tracks.
The passenger train travels at 60 mph. The freight
train travels at 30 mph. A passenger observes that it
takes 6 seconds to pass the freight train. How many
feet long is the freight train?
HINT: There are 5,280 feet in a mile.
Answer on page 77.
Souped-Up Survey
+.+
A survey agency reported their results in the local
newspaper. The report states that exactly one hun-
33
dred local lawyers were interviewed. Of the one hundred,
seventy-five lawyers own BMWs, ninety-five
lawyers own Volvos, and fifty lawyers own both a
BMW and a Volvo.
Within a short time after the report, several lawyers
argue that the survey results are incorrect. How can
they tell?
Toasty
•••
Answer on page 77.
In
sides of a bread slice for 30 seconds. His frying pan
can only hold two slices of bread at once. How can he
make three slices of French toast in only 1
instead of 2 minutes?
order to make French toast, Ricardo must fry both% minutes34
Now,
If 1 CA~ \rusTKE~r
oNE IN T~eAiR
AT ALL T,,\\ESAnswer on page
78.Circle Game
•• +
Examine the pattern of circles below. Can you place
the numbers one through nine in these circles so that
the sum of the three circles connected vertically, horizontally,
or diagonally is equal to fifteen?
Answer on page
78.A Fare Split
•• +
Michelle rents a car to take her to the airport in the
morning and return her home that evening. Halfway
to the airport, she picks up a friend who accompanies
her to the airport. That night, she and her friend
return back to Michelle's home. The total cost is
$20.00. If the amount to be paid is to be split fairly,
how much money should Michelle pay?
Answer on page
78.35
Pentagon Parts
•••
The pentagon below is divided into five equal parts.
Suppose you color one or more parts gray. How many
different and distinguishable patterns can you form?
Each pattern must be unique and not be duplicated
by simply rotating the pentagon.
Answer on page 79.
Bagel for Five?
•••
You and four friends have decided to split a bagel for
breakfast. The five of you are not fussy about the size
of the piece each will receive. In other words, all the
pieces don't have to be the same size.
D sing two perfectly straight cuts, is
divide this bagel into five pieces?
it possible toAnswer on page 79.
36
Coin Moves
•••
Place twelve coins in the pattern shown below. Notice
how they form the corners of six equal-sized squares.
Can you remove three of the coins to have only three
equal-sized squares remaining?
Answer on page 79.
Trapezoid Trap
•••
Divide the trapezoid below into four identical parts.
Answer on page 80.
37
A+Test
•••
Here's a math challenge of a different sort. Trace
these five shapes onto a sheet of stiff paper. Use a
pair of scissors to carefully cut them out. Then assemble
the shapes into a "plus" sign.
Answer on page 80.
Mis-Marked Music
•••
There are three boxes filled with audiocassette tapes.
One box contains rap tapes, another contains jazz
tapes, while the third contains both rap and jazz
tapes. All three boxes have labels identifying the type
38
of tapes within. The only problem is that all of the
boxes are mislabeled.
By selecting only one box and listening to only one
tape, how can you label all three boxes correctly?
Answer on page 80.
Measu
.r.i.n. g MugWithout the aid of any measuring device, how can you
use a transparent 16-ounce mug to measure a volume
of water that is exactly 8 ounces?
Answer on pages 80-81.
39
Coin RoD
......Two identical coins are positioned side by side. In
your mind's eye, roll the coin on the left (Coin A)
over the other coin (Coin B). When Coin A reaches
the opposite side of Coin B, stop. In which direction
will Coin Ns head be facing?
Now, let's suppose that Coin A rolls completely
around Coin B. If so, how many rotations does Coin
A make around its own center?
Answers on page 81.
Painting on the Side
......You are presented with several white cubes and a
bucket of red paint. To make each of them different,
you decide to paint one or more sides of each cube
red. How many distinguishable cubes can you make
with this painting method? Remember that any painted
side must be painted completely to make it distinguishable
from any other painted side.
Answer on page 81.
40
Magic Triangle
++.
Here's a magic triangle whose sides are formed by
sets of four numbers. To solve the puzzle, place the
numbers one through nine each in one of the circles.
When you are finished, the sums of all three sides
must be equal.
There are three different sums that can be used to
reach the solution. Can you find all three?
Answers on page 82.
41
Patterns
•••
The arrangement of numbers below represents a pattern.
This pattern is a mathematical relationship
between the numbers in each square, so don't look for
things like spelling, days of the week, cryptograms, or
codes. Can you uncover the pattern and fill in the
question mark in the last square?
Answer on page 82.
Frog Jump
•••
A frog falls into a well that is 18 feet deep. Every day
the frog jumps up a total distance of 6 feet. At night,
as the frog grips the slimy well walls, it slips back
down by 2 feet. At this rate, how many days will it take
the frog to jump to the rim of the well?
Answer on page 82.
42
Army Ants
•••
Two small armies of ants meet head-on along a jungle
path. Both armies would prefer to pass each other
rather than fight. There is a small space alo[lg the
side of the path. It is only large enough to hold one
ant at a time. Is it possible for the armies to pass each
other? If so, how?
~'t
_~r--'""-'
Answer on page 83.
43
No Sweat
•••
There are six players on a coed volleyball team. After
an exhausting game, each girl drinks 4 cups of water.
Each boy drinks 7 cups of water. The coach drinks 9
cups.
A total of 43 cups of water is consumed by everyone.
How many boys and how many girls are on the
team?
Answer on page 83.
Go Figure!
•••
In a distant planet, there are four forms of life beings:
zadohs, pugwigs, kahoots, and zingzags. All zadohs
are pugwigs. Some pugwigs are kahoots. All kahoots
are zingzags.
Which of the following statement(s) must then be
true?
1. Some zadohs are zingzags.
2. Some kahoots are zadohs.
3. All kahoots are pugwigs.
4. Some zingzags are pugwigs.
5. All zingzags are zadohs.
6. Some zadohs are kahoots.
Answer on page 84.
44
Square Pattern
•• -+
Suppose you have to paint all nine squares in the grid
below using one of three colors: red, blue, or green.
How many different patterns can you paint if each
color must be represented in every row and every column?
Each pattern must be unique. In other words, a
new pattern can't be made by simply rotating the
grid.
Answer on page 84.
Bouncing Ball,
•• +
Did you know that when a ball strikes the ground, its
shape distorts? This distortion stores the energy that
powers its rebound. The more its shape changes, the
higher the ball will bounce.
45
The ball in this puzzle rebounds to half the height
from which it is dropped. Suppose it is dropped from
a 1 meter height. What distance would the ball travel
before it comes to rest?
Answer on pages 84-85.
Complete the Pattern
•••
Use the pattern below to determine the value for X
andY
0
D ~ D 21D
0 ~ 0 18~
~ D ~ 35D
~ D D y21
26 30 xAnswer on page 85.
46
Checkerboard
•••
A full-size checkerboard has eight rows and eight
columns that make up its sixty-four squares. By combining
the patterns of these squares, you can put
together another 140 squares. The pattern below is
one-fourth the area of a full size checkerboard. What
is the total number of squares that are found in this
smaller pattern?
Answer on page 85.
Cutting
Edge•••
Kristin wants to remodel her home. To save money,
she decides to move a carpet from one hallway to
another. The carpet currently fills a passage that is 3
X
12 feet. She wishes to cut the carpet into two sec-47
tions that can be joined together to fit a long and narrow
hallway that is 2
look like?
x 18 feet. What does her cutAnswer on page 85.
The Die
Is. Cast•••
Which die is unlike the other three?
r
•;•~ ~;•}•I~
~
Answer on pages 85-86.
Playing
with Matches?•••
Thirty-two soccer teams enter a statewide competition.
The teams are paired randomly in each round.
The winning team advances to the next round. Losers
are eliminated. How many matches must be played in
order to crown one winner?
Answer on page 86.
48
Competiitg Clicks
......Let the Mouse Click Competition Begin!
Emily can click a mouse ten tim_es in 10 seconds.
Buzzy can click a mouse twenty times in 20 seconds.
Anthony can click a mouse five times in 5 seconds.
Assume that the timing period begins with the first
mouse click and ends with the final click. Which one
of these computer users would be the first to complete
forty clicks?
...
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Answer on page 86.
49WWW.NASA.COM7573.73.
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