Lateral Thinking 2
Number
& Math Play
73. How Many Students?
A new school has opened with fewer than 500
students. Onethird of the students is a whole number. So are onefourth,
onefifth, and oneseventh of the students. How many students go to this
school?
420 students: This is the only number under
500 that can be divided evenly by 3, 4, 5, and 7.
STRATEGY: Make a list.
Source: http://www.brainteasers.net,
August 27, 2000
Number & Math Play
74. How Old?
Mary is twice as old as her brother and half
as old as her father. In 22 years, her brother will be half as old as his
father. How old is Mary now?
Mary is now 22 years old.
From
"an ageold puzzle" reappearing in The World's Most Amazing Puzzles by
Charles Barry Townsend. New York : Sterling Publishing, 1993
Number & Math Play
75. Hungry Hamsters
Five hamsters — Arnie, Betty, Carl, Debby,
and Ernie — are learning to go through a maze. Each time a hamster reaches the
end of the maze, it gets a pellet of food.
So far, Arnie has gotten four more pellets
than Betty; Betty has gotten seven fewer pellets than Carl; Carl has gotten
five more pellets than Debby; and Debby has gotten three more pellets than
Ernie. Betty and Debby have gotten ten pellets between them.
How many times has
each hamster gone through the maze so far? (Each hamster has gone through more
than once.)
Arnie has gone through 8 times, Betty 4
times, Carl 11 times, Debby 6 times, Ernie 3 times. The key fact is that Betty
and Debby have gotten ten pellets between them.
There are only ten possible combinations that
will add up to ten pellets, and since we know that each hamster got more than
one pellet, we can eliminate four of them: Betty 0/ Debby 10, Betty 1/Debby 9,
Betty 9/Debby 1, and Betty 10/Debby 0. Try the remaining six combinations.
Betty 4/Debby 6 is the only one that will work.
Source:
Barnes and Noble, Mensa
Presents Mind Games for Kids, p.13
Number & Math Play
76. Insects and Spiders
As you know, one way to tell an insect from a
spider is to count its legs. All insects have six legs, and all spiders have
eight legs. So if some insects and spiders went to a dance, and there were 48
dancing legs, how many insects and how many spiders were at the dance?
Four insects (24 legs) and three
spiders (24 legs). No other combination will work.
Number & Math Play
77. Loose Change
I have pennies,
nickels, dimes, and quarters. How many of which coins should I give you if you
want 1 dollar in 6 coins? How many of which coins should I give you if you want 1
dollar in 28 coins?
If you want 1 dollar in 6 coins, I should
give you 3 quarters, 2 dimes, and 1 nickel.
If you want 1 dollar in 28 coins, I should
give you 3 quarters and 25 pennies.
From The Best of Brain Teasers from Teacher
Created Materials, p. 141
Number & Math Play
78. Magic Square
Fill in the missing numbers so that the
numbers in every row, down, across, and diagonally, will add up to 30.
Then, for a real challenge, make up your own
magic square.
12

16


4

8

12

2

16

14

10

6

4

18

8

Number and Math Play
79. Minus Two
How many times can you subtract
the number 2 from the number 32?
Once. After you subtract 2 from
32, you subtract 2 from 30, from 28, and so on.
Source: Inspired by a puzzle in Mensa
Presents Mighty Brain Teasers, R. Allen & J. Fulton. Number & Math Play
80. Missing Number
What is the number missing from the following
sequence?
4 7 11 18 29 47 ____ 123 199 322
The missing number is 76. Beginning with the
third number in the sequence, each number is the sum of the two preceding
numbers.
STRATEGY: Look for a pattern.
Source: Puzzle 13 (p. 8) in IQ Puzzles, compiled by Joe
Cameron, Number & Math Play
81. Odd One Out
Which number on this square is the odd one
out? Why?
3

33

15

36

12

27

34

18

72

39

30

6

24

21

9

42

34.
All
the other numbers are evenly divisible by 3.
STRATEGY:
Look for a pattern.
Source:
Scholastic, Mensa Number Puzzle for Kids, puzzle 141
Number and Math Play
82. Odd Balls
Suppose you have 7 balls and 2 paper bags.
How can you put an odd number of balls into each bag?
Put 3 balls in each bag (or put 1 ball in the
first bag and five in the second). What about the seventh ball? Just don't put
it into a bag at all!
Source:
Usborne Brain Puzzles, p. 14
Number and Math Play
83. Painting by the Numbers
Two painters can paint two rooms in two
hours. If 12 rooms have to be painted in six hours, how many painters do you
need?
The two painters need one hour to paint one
room. In six hours, the original two painters can paint six rooms. You'll have
to double the number of painters to four if you want twelve rooms painted in
six hours.
STRATEGY: Make it simpler.
Source:
Puzzle 34 (p. 28) in IQ
Puzzles, compiled by Joe Cameron, New York: Barnes & Noble, 2000
Number & Math Play
84. Penny Candy
Back in the days when candy cost just a few
cents a piece, Alice was able to buy exactly 100 pieces of candy for a dollar.
Some of her candy cost 10 cents a piece; some of her candy cost 3 cents a piece;
and some of her candy cost 1 penny for 2 pieces.
How many pieces of each price candy did Alice
buy?
5 pieces of candy at 10 cents a piece equals
50 cents
1 piece of candy at 3 cents a piece equals 3
cents
94 pieces of candy at 2 pieces for 1 penny equals 47 cents
100 pieces equals $1.00
94 pieces of candy at 2 pieces for 1 penny equals 47 cents
100 pieces equals $1.00
STRATEGY: Guess and check.
Number & Math Play
85. Pennies
If someone offered you a choice between a ton
of pennies and five miles of pennies lined up with touching edges, which would
you take if you wanted the most money? Here are some facts to help you decide:
A penny weighs .09
ounces.
A penny's diameter is .75 inches.
A penny's diameter is .75 inches.
Five miles of pennies are worth more than the
ton of pennies. Use a calculator to find the inches in a mile, then 5 miles.
316,800 inches divided by .75 inches = 422,400 pennies, or $4,224. 1 ton =
32,000 ounces divided by .09 ounces = 355,555.55 pennies, or $3,555.56.
Number & Math Play
86. Piano Lessons
Abigail, Bettina,
Cynthia, and Dahlia all began piano lessons last year. Cynthia took twice as
many lessons as Bettina. Abigail took 4 lessons more than Dahlia but 3 fewer
than Cynthia. Dahlia took 15 lessons altogether.
How many lessons did Bettina take?
Bettina took 11
lessons.
Let A stand for Abigail, B for Bettina, and
so on. C = 2B A = D + 4 = C  3 D = 15
Since D = 15, you know that A = 19. You also
know that C  3 = 19, which means that C = 22. And since C = 2B, 22 = 2B, which
means that B = 11.
Source: Inspired by a similar puzzle in Unriddling by Alvin
Schwartz, New York: Lippincott, 1983
87. Pick a Pair
Ben has socks in five
different colors: two pairs of blue socks, two pairs of black, three pairs of
brown, four pairs of green, and four pairs of white. Ben, who is not very neat,
doesn't bother to pair up his socks when he puts them away. He just throws them
in the drawer. Now Ben is packing to go away for the weekend, but there's been
a power failure and he can't see the socks in his drawer.
How many socks does he have to take out of
his drawer to be sure he has at least two that will make a pair?
The answer is six
socks. If Ben takes out five socks, he could have one of each color, with no
two matching colors. But if he takes out six socks, two have to be the same
color, since there are only five colors. (Sorry we tricked you with all that
unnecessary information!)
Number & Math Play
88. Profit or Loss?
Jill brought home a
poster from her trip. She had paid $25 for it. Liu saw the poster and gave Jill
$35 for it. A few days later, Jill bought the poster back for $45. Then she
sold it again, this time to her cousin Allie for $55.
Did Jill make money on her transactions, or
lose money?
Add up all the money that Jill spent — $25
and $45 for a total of $70. Then add up all the money Jill got for the poster —
$35 and $55 for a total of $90. Jill came out ahead by $20.
Source: Inspired by a puzzle in Put on Your Thinking Cap,
Helen Jill Fletcher. New York: AbelardSchuman, 1968Number & Math Play
89. Puzzle about Puzzles
Ann, a very
competitive person, decides to give herself 2 points for every crossword puzzle
in her daily newspaper that she completes correctly and to forfeit 3 points for
every crossword in the paper that she completes incorrectly or cannot complete.
After 30 days of working the puzzles, Ann has
a score of zero. How many puzzles has she solved correctly?
Ann solved 18 puzzles
correctly; therefore, at 2 points a puzzle, she earned 36 points. But Ann
failed to solve 12 correctly; therefore, at 3 points a puzzle, she lost 36
points.
In order to arrive at a total of 0 points,
the total points for correctly and incorrectly solved puzzles must be equal.
Since Ann loses more points for an incorrect puzzle than she gains for a
correct one, you know she has to solve more correctly than incorrectly. That
means she has to have more than 15 correct puzzles and less than 15 incorrect
ones, since the total number of puzzles is 30.
Try out 16 correct (gain 32 points) and 14
incorrect (lose 42 points). That's wrong because it would leave Ann with 10
points. Try 17 correct (gain 34 points) and 13 incorrect (lose 39 points). It
still doesn't come out even. Try 18 correct (gain 36 points) and 12 incorrect
(lose 36 points). Bingo!
Source: Carter & Russell, Classic Brain
Teasers, p.53Number & Math Play
90. Rain, Rain, Every Day
Randy's science
project was making a rain gauge to measure the amount of rain for one week. It
rained each day that week, starting on Monday, and each day the amount of rain
in the gauge doubled. By the following Sunday, the rain gauge was completely
filled. On which day was the rain gauge halffilled?
Randy's rain gauge
was halffilled on Saturday. It doubled on Sunday, to become completely filled.
STRATEGY: Draw a picture.
Source:
Usborne Brain Puzzles, p. 6Number and Math Play
91. Right in the Middle
The numbers in the
middle column are related in some way to the numbers in the left and right
columns. How are they related?
3

42

8

5

51

3

8

61

2

7

53

5

In each row, the
middle number is the product of the number on its left and the number on its
right, but backwards.
STRATEGY: Look for a pattern.
Source:
Scholastic, Mensa Number Puzzle for Kids, puzzle 184Number & Math Play
92. Roman Values
What is the second to
the largest number and the second to the smallest number that you can make if
you have one each of the following Roman numerals?
I V L X
The second to the
largest number is LXIV (64); the second to the smallest number is XLVI (46).
STRATEGY: Make a list.
I = 1
V = 5
L = 50
X = 10
The only combinations are: 44, 46, 64, 66
Inspired
by a puzzle in Mighty Mini Mind Bogglers, K. C. Richards, New York: Sterling,
1999I = 1
V = 5
L = 50
X = 10
The only combinations are: 44, 46, 64, 66
Number & Math Play
93. Sale!
An online shopping
site reduced the price of one computer model by 25 percent for a sale. By what
percentage of the sales price must it be increased to put the computer model
back at its original price?
Suppose the computer
originally cost $100.00. With the 25% deduction, it would cost $75.00. To bring
the price back to the original $100.00, you'd have to add $25.00, which is 1/3
of $75 — or 33.3%.
Source:
Cameron,
IQ Puzzles, p. 40Number & Math Play
94. Six Daughters
Mr. Seibold has 6
daughters. Each daughter is 4 years older than her next younger sister. The
oldest daughter is 3 times as old than her youngest sister.
How old is each of the daughters?
From youngest to
oldest, the 6 daughters are 10, 14, 18, 22, 26, and 30.
Source:
Inspired by a puzzle in Put on Your Thinking Cap, Helen Jill Fletcher. New
York: AbelardSchuman, 1968Number & Math Play
95. Spiders and Insects
Once the spiders and
the insects played a game of tag. To be fair, the insects were allowed to have
more members on their team, because an insect has fewer legs than a spider. (As
you know, a spider has eight legs, while an insect has only six.) Altogether,
there were 20 heads and 136 legs in the game.
How many insects were playing? How many
spiders?
8 spiders, 12 insects
You know there are 20 animals, and more
insects. If all were insects, there would be 120 legs. But there are 136, which
means that 16 additional legs must belong to spiders. Since each spider gets 2
of those 16 legs, divide 16 by 2 to get 8 spiders. Subtract 8 from 20 to get 12
insects.
STRATEGY: Work backwards.
Source: Barnes and Noble, 100 Numerical Games, Pierre
BerloquinNumber & Math Play
96. Stack 'Em Up
Kenny had an
afterschool job at the Pet Food Emporium. His boss told him to stack 35
cartons of dog food so that each row of cartons would have one more than the
row above it. How many rows of cartons did Kenny have when he was finished?
7 rows. 8 cartons in
the bottom row, 2 in the top
Number and Math Play97. Summit
You are at a point
near the top of a mountain that you have been climbing. In normal conditions,
you would need to take only 5 more steps forward to reach the summit. Today,
though, the wind is posing problems. For each 2 steps you take forward, the
wind pushes you back 1 step. What is the total number of forward steps that you
will have to take from this point to reach the summit in this windy weather?
Allowing for being
pushed backward, you will have to take a total of 8 forward steps to reach the
summit. STRATEGY: Draw a picture or diagram.
Number & Math Play
98. Super Sevens
For each of the seven
rows, insert the mathematical symbols (+, , ÷, ×) that will make the equation
correct for someone calculating from left to right. Here's an example with the
symbols already inserted:
7
× 7  7 ÷ 7 = 6
7
7 7 7 = 9
7 7 7 7 = 15
7 7 7 7 = 56
7 7 7 7 = 63
7 7 7 7 = 91
7 7 7 7 = 147
7 7 7 7 = 294
7 7 7 7 = 15
7 7 7 7 = 56
7 7 7 7 = 63
7 7 7 7 = 91
7 7 7 7 = 147
7 7 7 7 = 294
7 + 7 ÷ 7 + 7 = 9
7 ÷ 7 + 7 + 7 = 15
7 ÷ 7 + 7 × 7 = 56
7 × 7 + 7 + 7 = 63
7 + 7 × 7  7 = 91
7 + 7 + 7 × 7 = 147
7 × 7  7 × 7 = 294
Source:
Will Shortz's
Best Brain Busters, p. 97 (and other sources)7 ÷ 7 + 7 + 7 = 15
7 ÷ 7 + 7 × 7 = 56
7 × 7 + 7 + 7 = 63
7 + 7 × 7  7 = 91
7 + 7 + 7 × 7 = 147
7 × 7  7 × 7 = 294
Number & Math Play
99. The Largest Roman
What is the largest
number you can express in Roman numerals if you have one each of the following
letters? (NOTE: You cannot use any of the letters as powers or exponents.)
C D I L M V X
MDCLXVI (1,666)
Number & Math Play
100. The Wall
If the Jones twins
can build a wall five bricks long and five bricks high in 1 minute, how long
will it take them to build a wall ten bricks long and ten bricks high?
The first wall has 25
bricks. The second wall has 100 bricks — four times as many. So it will take
four times as long — that is, four minutes.
Source:
David Adler, Easy
Math Puzzles Number & Math Play
101. Teaming Up
In Ms. Quimby's
class, everyone plays on a team. There are five more soccer players than
baseball players. There are three more students on the track team than on the
baseball team. There are two more football players than hockey players. There
are three more students on the track team than on the football team. The number
of baseball and football players equals 8.
How many players are on each team? How many
students are there in the class?
The three key pieces
of information are (1) there are three more students on the track team
than on the baseball team; (2) there are three more students on the
track team than on the football team (therefore the number of students on the
baseball team and the football team are the same); and (3) the number of
baseball and the number of football players equals 8. Since the two numbers are
equal, there must be four players on each team. Now it's easy to figure out the
rest.
Source:
Barnes and Noble, Mensa
Presents Mind Games for Kids, p. 89Number & Math Play
102. Time Difference
Larry's flight is
supposed to leave Sydney, Australia, at 1 p.m. on Thursday, September 9. What
time and what day will Larry get to New York City?
New York is twelve hours behind Sydney; that
is, it's twelve hours later in Sydney than in New York City. The flight from
Sydney to Los Angeles takes 14 hours, Larry's layover in Los Angeles is 2
hours, and the flight from L.A. to New York is 5 hours. Assume there are no delays.
Larry will get to New
York City on Thursday, September 9, at 10 p.m.
Source:
Karen C. Richards,
Mighty Mini Mind Bogglers, p. 79Number & Math Play
103. Time Puzzle
Two hours ago, it was
as many hours after one o'clock in the afternoon as it was before one o'clock
in the morning.
What time is it now?
It's now nine o'clock
in the evening.Number and Math Play
104. Time to Paint the Floor
If it
takes Polly the Painter 1 hour to paint a bedroom floor that is 9 feet wide and
12 feet long, how long will it take her to paint the living room floor, which
is twice as wide and twice as long?
Four
hours. The size of a room that measures 9’ x 12’ is 108 square feet. A room
that is twice as long and twice as wide will measure 18’ by 24’, which makes
432 square feet. That makes the living room 4 times the size of the bedroom, so
it will take 4 times as long to paint.
Number & Math Play105. Time Will Tell
Picture a regular
(analog) clockface — with the numerals 1 to 12 correctly positioned.
Where would you draw a straight line to split
the clockface in half in such a way that the sum of the numbers on one side of
the line will equal the sum of the numbers on the other side of the line?
Draw a straight line
that begins on the left side of the clockface between 9 and 10 and cuts across
the clockface to the right side between 3 and 4. The sum of the numbers above
the line equals 39, and the sum of the numbers below the line equals 39.
Based on a
puzzle in
The World's Best Puzzles by Charles Barry Townsend. New York: Sterling
Publishing, 1986.Number & Math Play
106. Tug of War
The young farm
animals have been playing tug of war. With 3 piglets on one side and 2 kids
(young goats) on the other side, the game ended in a tie. Similarly, with 3
calves on one side and 4 kids on the other side, the game ended in a tie. Which
side, if either, will win if one side has 5 piglets and the other side has 2
calves?
The 5 piglets will
win. If there were only 4 piglets on one side and 2 calves on the other side,
it would be a tie.
Here's one way to solve the puzzle. The
puzzle tells you the following:
2
kids = 3 piglets
3 calves = 4 kids
Those
facts mean the following are also true:
4
kids equal 6 piglets
3 calves equal 6 piglets
Therefore,
1 calf = 2 piglets. It follows that 2 calves = 4 piglets. If 2 calves and 4
piglets would tie, then 5 piglets would beat 2 calves.
Source:
Karen C. Richards, Mighty
Mini Mind Bogglers, p. 11Number & Math Play
107. Two Legs, Four Legs
A puzzle maker looks
out a window into his back yard. He sees a mix of boys and cats. He counts 22
heads and 68 legs. He wants YOU to figure out how many boys are in the yard.
The boys plus the
cats have a total of 22 heads. Or B + C = 22. Subtracting C from each side of
the preceding results in a value for B of 22  C.
The boys' legs equal two times the number of
boys, the cats' legs equal four times the number of cats, and the total number
of legs equals 68. Or 2B + 4C = 68. Using the value for B already calculated,
the last equation can be rewritten as 2 (22  C) + 4C = 68, or 44  2C + 4C =
68, which, by addition and subtraction, becomes 2C = 24, or C = 12.
There
are 12 cats and 10 boys in the back yard.
From a
puzzle in Puzzles,
Patterns, and Pastimes: From the World of Mathematics by Charles F. Linn.
Garden City: Doubleday, 1969Number and Math Play
108. Uphill, Downhill
Grandma
walked up a hill at the rate of 2 miles an hour, turned around as soon as she
got to the top, and walked down the hill at the rate of 4 miles an hour. The
whole trip took her 6 hours. How many miles is it to the top of the hill?
Here's
one of several ways to figure out the answer: Grandma walked 1 mile up the hill
in 30 minutes and 1 mile down in 15 minutes. In other words, 1 mile took her 45
minutes round trip. The whole trip took her 6 hours, or 360 minutes; if you
divide the overall time (360 minutes) by the time it took to do 1 mile (45
minutes), you find out that the overall length of the hill is 8 miles.
STRATEGY: Make it simpler.
Source:
Inspired by a puzzle in The Adler Book of Puzzles and Riddles, or Sam Loyd
UptoDate, Irving and Peggy Adler. New York: John Day, 1962Number & Math Play
109. Walking the Dogs
A group of kids got
together and started a dogwalking business. They got lots of clients right
away, so that when they all walked their dogs together, there were twelve heads
and forty legs. How many kids and how many dogs were out walking?
If all 12 heads
belonged to kids, there would be 24 legs (2 legs for each head). But there are
40 legs. That leaves 16 legs, or 8 pairs of legs that must belong to dogs. So
there are 8 dogs. Subtract 8 from 12 (since everyone has only one head), and
that leaves 4 kids.
Number and Math Play
110. What Time Is It?
What is
the number missing from the following sequence?
By figuring out the relationship of these watch settings to one another, you should be able to determine what time will show up on Watch E.
By figuring out the relationship of these watch settings to one another, you should be able to determine what time will show up on Watch E.
WATCH A 5:23
WATCH B 8:26
WATCH C 12:30
WATCH D 5:35
WATCH E ______
WATCH B 8:26
WATCH C 12:30
WATCH D 5:35
WATCH E ______
The
hours move ahead 3, 4, and 5 hours. The minutes move ahead 3, 4, and 5 minutes.
The time WATCH E will show is 11:41, 6 hours and 6 minutes beyond 5:35.
STRATEGY: Look for a pattern.
Source:
Inspired by a puzzle in Mensa Presents Mighty Brain Teasers, R. Allen & J.
Fulton. New York: Barnes and Noble, 1999STRATEGY: Look for a pattern.
Number and Math Play
111. What's the Fewest?
Some kids are playing
hide and seek in a park where there are seven trees. One of the kids is “It,”
and the others are all hiding behind trees. Of course, you can’t see them,
because they’re hiding. See if you can figure out the fewest possible kids
hiding, using the following information:
A girl is hiding to the left of a boy.
A boy is hiding to the left of a boy.
Two boys are hiding to the right of a girl.
A boy is hiding to the left of a boy.
Two boys are hiding to the right of a girl.
The fewest kids
hiding is 3. A girl is on the left; to her right is a boy; to his right is
another boy.
STRATEGY: Draw a picture or diagram.
Number & Math Play
112. What's So Special?
What's special about the number 2520?
HINT: The answer has something to do with the numbers 1 through 10.
The number 2520 is
the smallest number that can be divided evenly by each of the numbers 1 through
10.
Source:
Carter & Russell,
Classic Brain Puzzlers, p. 57Number & Math Play
113. What's Your Sign?
In the equation
below, replace each question mark with one of the four mathematical signs: +,,
×, or ÷. Each sign can be used only once. Fill in the blanks to solve the
equation. (Hint: the first sign is +.)
7
? 5 ? 4 ? 7 ? 6 = 15
(7 + 5) ÷ 4 × 7  6 =
15
If
the first sign is +, there are only 6 possible combinations. You can get the
answer by trying each one of them out. There is only one correct answer.
Source:
Barnes and Noble,
Mensa Mind Games for Kids, p. 18Number and Math Play
114. Wheel of Fortune
A game wheel shows
the numbers 1 to 36. Figure out on which 2digit number Lucy has landed given
the following facts:
The number is divisible by 3.
The sum of the digits in this number lies between 4 and 8.
It is an odd number.
When the digits in this number are multiplied together, the total lies between 4 and 8.
The sum of the digits in this number lies between 4 and 8.
It is an odd number.
When the digits in this number are multiplied together, the total lies between 4 and 8.
Lucy has landed on
15. Make a list of numbers 1 36 that are divisible by 3. Cross out all that
are even. This leaves 9, 15, 21, 27, and 33. 9, 21, and 27 have a “sum of
digits” less than 4 or more than 8. But, 1 x 5 = 5 and 3x 3 = 9.
STRATEGY: Make a list and search for a
pattern.
Word & Letter Play115. When, Oh, When?
Ken promised Ben
today to tell him a big secret on the day before five days from the day after
tomorrow. Today is Saturday, October 21. On what day and date will Ken tell Ben
the secret?
Ken will tell Ben the
secret on Friday, October 27Number and Math Play
116. Where's the Fruit Juice?
A catering company
sells large containers of iced tea and large containers of fruit juice. Right
now the company has six containers, each holding the following amounts:
Container
A: 30 quarts
Container B: 32 quarts
Container C: 36 quarts
Container D: 38 quarts
Container E: 40 quarts
Container F: 62 quarts
Container B: 32 quarts
Container C: 36 quarts
Container D: 38 quarts
Container E: 40 quarts
Container F: 62 quarts
Five
of the containers hold iced tea, and one container holds fruit juice.
Two
customers come into the shop. The first customer buys two containers of iced
tea. The second customer buys twice as much tea as the first customer. Which
container is holding the fruit juice?
Container E holds the
fruit juice. The second customer can buy twice as much as the first customer if
the first customer buys Containers A and C (for a total of 66 gallons) and the
second customer buys Containers B, D, and F (for a total of 132 gallons).
Therefore, the remaining container—E—must hold the fruit juice.
STRATEGY: Make a list of possibilities
Number & Math Play
117. Which Wages?
A man applied for a
job. The woman who interviewed him offered him two pay rates: a straight rate
of $100 a day or a pay rate that would begin at one cent the first day and then
double each day. The second rate meant the man would earn two cents the second
day, four cents the third day, eight cents the fourth day, and so on. The man
chose the second rate, and the woman hired him.
Tell why, and prove your case.
The woman hired the
man because she wanted a smart employee, and he was smart enough to figure out
that he would accumulate much more money at the second pay rate as soon as he
got to the 18th day of work. It's true that at Day 10, the first rate would pay
him a total of $1,000, for the first 10 days and the second rate would pay him
a total of only $10.23 for the same ten days. By day 19, however, the first
rate would earn him a total of $1,900, but the second rate would earn him
$2,621.44 just for that day! And the man's earnings would keep increasing by
leaps and bounds.
Source: The Best of Brain Teasers from Teacher
Created Materials, p.127Number & Math Play
118. Wrap It Up
You have 100 yards of
ribbon on a spool, and you need 100 lengths of ribbon 1 yard long. It takes you
1 second to measure and cut each yard. How long will it take you to come up
with the 100 pieces of ribbon?
It will take you 99
seconds. Each cut, including the 99th, produces two pieces of ribbon.
Source:
Carter & Russell,
Classic Brain Puzzlers, p. 80Reasoning
119. Catchy Code
The message below is
written in code. Each letter of the alphabet is represented by a sign and a
number. The words are separated by lines like this:
___. See if you can break the code and read
the message.
This
is a catchy one, so here are two hints:
Hint
1: Do the signs look familiar? Think about where you’ve seen them. That’s the
key.
Hint 2: Notice that the only numbers that appear in the code are 1, 2, and 3. They stand for rows—row 1, row 2, and row 3.
(To get you started, ^1 stands for Y, ^2 stands for H, and ^3 stands for N.)
Hint 2: Notice that the only numbers that appear in the code are 1, 2, and 3. They stand for rows—row 1, row 2, and row 3.
(To get you started, ^1 stands for Y, ^2 stands for H, and ^3 stands for N.)
(2
(1 (1 *2 ___ $2 (1 $1 ___ %1 ^2 #1 @2 #1 ___@2 *1 %2 ^3 @2
___(1 ^3 ___ ^1 (1 &1 $1 ___ #3 (1 &3 )1 &1 %1 #1 $1 ___
*2 #1 ^1 %3 (1 !2 $1 #2.
___(1 ^3 ___ ^1 (1 &1 $1 ___ #3 (1 &3 )1 &1 %1 #1 $1 ___
*2 #1 ^1 %3 (1 !2 $1 #2.
The answer is: Look
for these signs on your computer keyboard. And that’s also the key to the code.
!2 stands for the letter A because A is down two rows (going diagonally from
left to right) from the exclamation point on your keyboard. !1 would stand for
the letter Q, and !3 would stand for the letter Z. Here’s the whole code:
!1
= Q; !2 = A; !3 = Z
@1 = W; @2 = S; @3 = X
#1 = E; #2 = D; #3 = C
$1 = R; $2 = F; $3 = V
%1 = T; %2 = G; %3 = B
^1 = Y; ^2 = H; ^3 = N
&1 = U; &2 = J; &3 = M
*1 = I; *2 = K;
(1 = O; (2 = L
)1 = P
@1 = W; @2 = S; @3 = X
#1 = E; #2 = D; #3 = C
$1 = R; $2 = F; $3 = V
%1 = T; %2 = G; %3 = B
^1 = Y; ^2 = H; ^3 = N
&1 = U; &2 = J; &3 = M
*1 = I; *2 = K;
(1 = O; (2 = L
)1 = P
Reasoning
120. Doggies
The dog named Jam is
heavier than the dog named Jelly.
Copper weighs more than Brandy but less than
Pumpkin.
Brandy weighs more than Jelly.
Pumpkin weighs less than Jam.
Brandy weighs more than Jelly.
Pumpkin weighs less than Jam.
List the dogs in the order of their weights,
starting with the heaviest.
The heaviest dog is
Jam, the next heaviest is Pumpkin, the next heaviest is Copper, the next
heaviest is Brandy, and the least heavy (or the lightest) is Jelly.
STRATEGY: Guess and check  write
each name on notecards and move them to test sequence
Reasoning121. Escape Hatch
SETTING: A prison cell with a
dirt floor, stone walls, no window but a skylight very high up in the ceiling;
no furniture except for a mattress
ACTION: The prisoner who was
in the cell manages to escape through the skylight.
QUESTION: How did the prisoner
escape?
First, the prisoner
dug a hole in the dirt floor. Second, the prisoner piled the dirt from the hole
against the wall. Third, the prisoner climbed the pile of dirt and escaped
through the skylight.
Based on a
puzzle in
More Puzzles for Pleasure and Leisure by Thomas L. Hirsch. New York:
AbelardSchuman, 1974.Reasoning
122. Flat Tire
Two friends were
driving on the highway when they got a flat tire. First they took off the
hubcap. Then they unscrewed the four lug nuts — the screws that hold the tire
in place. They put the inverted hubcap down on the road and carefully placed
the lug nuts inside the hubcap. Then they removed the flat.
As they were in the process of putting on the
spare tire, another car came along, hitting the hubcap and scattering the four
lug nuts where they could not be found. The driver of the other car felt sorry,
so he stopped to help. The two friends followed his advice, and in a little
while they were back on the road again. What did the man tell them?
The man told the two
friends to take one lug nut off each of the other three tires and use them to
hold the spare tire in place. (Later they could buy four more lug nuts so that
each tire would have four again.)
Reasoning
123. Getting Across
Ms. Waters and her
twins, Danny and Anny, want to cross from the east side of the river to the
west side in a canoe. But the canoe can hold no more than 200 pounds. Ms.
Waters weighs 160 pounds, and Danny and Anny weigh 100 pounds each.
How can all three of them reach the other
side of the river in the canoe?
First the twins
paddle to the west side of the river. Anny stays on the west side, and Danny
comes back. Mrs. Waters rows alone to the west side, leaving Danny on the east
side. Finally, Anny comes back for Danny.
Together, they paddle to the west side of the
river. (You can reverse Anny and Dannyit doesn't matter which one goes first.)
Reasoning
124. How Many Were Going To Saint Ives?
This is a very old
rhyming riddle. See if you can answer it by reading and thinking very
carefully.
As I was going to Saint Ives,
I crossed the path of seven wives.
Every wife had seven sacks,
Every sack had seven cats,
Every cat had seven kittens,
Kittens, cats, sacks, wives,
How many were going to Saint Ives?
I crossed the path of seven wives.
Every wife had seven sacks,
Every sack had seven cats,
Every cat had seven kittens,
Kittens, cats, sacks, wives,
How many were going to Saint Ives?
Only one person was
going to Saint Ives.
If
he or she crossed the path of the seven wives, then the kittens, cats, sacks,
and wives were all going in a different direction!
(If
everyone was going in the same direction, however, the answer would be 2,801 —
7 wives, 49 sacks, 343 cats, and 2,401 kittens equal 2,800. Then you have to add
one more for the person speaking the words of the riddle.)
Reasoning
125. Moving Day
The Masters family is
moving to a new house. They have a dog, a cat, and a pet mouse, but the animals
don't get along in the car, so they can take only one at a time.
Then there are other problems. They can't
leave the dog alone with the cat, because the dog chases the cat if no one is
watching. And they can't leave the cat and the mouse together, because...well,
you know what would happen if they did.
How can the Masters family get all three of
their pets to their new house?
They take the cat to
the new house, leaving the dog and the mouse at the old house. They return to
the old house and take the mouse to the new house. They take the cat back to
the old house, leave it there, and take the dog to the new house. Then they
return to the old house for the cat.
Reasoning
126. Mystery Twins
Two babies born on
the same day in the same year with the same mother and father are not twins.
Can you explain how this can be?
The two babies are
two of a set of triplets.
Reasoning
127. Not Enough Time
Larry insists that he
does not have enough time to go to school more than 17 days a year. He comes to
this conclusion based on the following list that he put together.
Activity

Number of days
per year 

Sleep (8 hours a day)

122


Meals (2 hours a day)

31


Weekends

104


Summer vacation

60


Recreation (2 hours a day)

31


Total

348

Inspired
by the list, Larry claims he has only 17 days left in the year for school.
What's wrong with his thinking?
Larry's categories
overlap. For example, he has counted 60 days for vacation, during which time he
will both eat and sleep, activities that he has already counted separately. The
60 vacation days also include weekends, another category that he has already
counted separately. He should not count the same periods of time more than
once.
Inspired
by a puzzle in Mathematical
Puzzles by Martin Gardner. New York: Thomas Y. Crowell Company, 1961.Reasoning
128. Puzzling Relations
A man named George
was hurrying to get ready for a dinner party when Dan rang his doorbell.
"I'm just rushing off to a dinner
party," said George, "but I'm sure it would be fine if you came
along."
So the two went off together. When they
arrived at the party, George, who always enjoyed getting people to use their
heads, introduced Dan to the other guests with the following rhyme:
"Brothers and sisters have I
none,
But this man's father is my father's son."
But this man's father is my father's son."
How were George and Dan related?
Dan was George's son.Reasoning
129. Relabeling
In front of you are
three covered cartons. One is labeled mustard packets; one is labeled ketchup
packets; one is labeled mustard and ketchup packets. None of the
cartons is correctly labeled.
How can you relabel the cartons correctly if
all you're allowed to do is close your eyes, reach into one carton, take out
one packet, and then look at it?
You can solve this
brainteaser by one of the following scenarios:
You already know the carton mislabeled mustard
and ketchup packets must contain only mustard packets or only ketchup
packets. If the packet you open is mustard, you should relabel the carton you
took it from mustard packets. Since you've already used up the label mustard
packets, the carton mislabeled ketchup packets cannot possibly
contain only mustard packets; since it is mislabeled, it can't contain only
ketchup packets; so you should relabel it mustard and ketchup packets.
Therefore, the remaining carton to be relabeled as ketchup packets; it's the
only possibility left.
or
You
already know the carton mislabeled mustard and ketchup packets must
contain only mustard packets or only ketchup packets. If the packet you open is
ketchup, you should relabel the carton you took it from ketchup packets.
Since you've already used up the label ketchup packets, the carton
mislabeled mustard packets cannot possibly contain only ketchup packets;
since it is mislabeled, it can't contain only mustard packets; so you should
relabel it mustard and ketchup packets. Therefore, the remaining carton
to be relabeled as mustard packets; it's the only possibility left.
Based on a
brainteaser posted on April 8, 1999, on www.brainteasers.net.Reasoning
130. Ripping Pages
If you ripped the
following pages out of a book, how many separate sheets of paper would you
remove? The page numbers are 4, 5, 24, 47, and 48.
You would have four
sheets of paper. The odd pages of a book are on the right side, and the even
pages are on the left. Therefore, pages 47 and 48 are opposite sides of the
same sheet of paper.
Source:
Sterling Pocket Puzzlers, Brain Teasers, p.20Reasoning
131. Round vs. Square
Why is it better for manhole covers to be round rather than square?
You can turn a square
manhole cover sideways and drop it down the diagonal of the manhole. You cannot
drop a round manhole cover down the manhole. Therefore, round manhole covers
are safer and more practical than square ones.
Based on
"Manhole Covers," found at http://einstein.et.tudelft.nl/~arlet/puzzles/lateral.html, which cites Challenging Lateral Thinking Puzzles by Paul Sloane and Des MacHale, distributed by Cassell in the UK and by Capricorn Link in Australia.
Reasoning
132. Sisters & Brothers
Suppose I have two
siblings, and at least one of them is a girl. What are the odds that I have two
sisters? Supposing I have two siblings, and the older one is a boy. What are
the odds that I have two brothers?
The probability that
both are girls is 1/3. (The odds that both are girls is 1 to 2 one way it can
be true against two ways it can not.) There are four possibilities when
considering the gender of two siblings: girlgirl, girlboy, boygirl, and
boyboy. Given that I have one sister, the boyboy combination is impossible.
So in this case, there are three possible combinations, and only one with both
girls.
In the second case, the probability of having
two brothers is 1/2. (The odds are "even"  1 to 1.) The same four
possibilities for gender must be considered. Girl girl is not possible from
the given information. The statement "the older one is a boy" also
eliminates the girlboy option. This leaves only two choices.
STRATEGY: Draw a picture or diagram.
Reasoning
133. The Barbershop Puzzle
A traveler arrives in
a small town and decides he wants to get a haircut. According to the manager of
the hotel where he's staying, there are only two barbershops in town — one on
East Street and one on West Street. The traveler goes to check out both shops.
The East Street barbershop is a mess, and the barber has the worst haircut the
traveler has ever seen. The West Street barbershop is neat and clean; its
barber's hair looks as good as a movie star's.
Which barbershop does the traveler go to for
his haircut, and why?
The traveler goes to
have his hair cut at the barbershop on East Street. He figures that since there
are only two barbershops in town the East Street barber must have his hair cut
by the West Street barber and vice versa. So if the traveler wants to look as
good as the West Street barber (the one with the good haircut), he'd better go
to the man who cuts the West Street barber's hairthe East Street barber.
By the way, the reason the West Street
barbershop is so clean and neat is that it seldom gets customers.
Source: A Haircut in Horse
Town, p.64 (and other sources)Reasoning
134. There's Something Fishy Going On
Although each of the
following sentences sounds okay at first, there's really something wrong with
each one of them. Read the sentences and explain why each one is a little
"fishy."
1.
No
one goes to that restaurant any more because it's too crowded.
2.
I'm glad I don't like spinach, because
if I liked it, I'd eat it, and it tastes awful.
3.
If you can't read this sign, ask for
help.
1.
If no
one goes to the restaurant, it can't be crowded.
2. If the person did like spinach, he or she
wouldn't think it tasted awful.
3.
If the person can't read the sign, she or her won't know that it says to ask
for help.
Reasoning
135. Toast for Three
Dad is preparing
breakfast for his three children—Dan, Ed, and Frank. Each boy wants Dad to
toast 1 slice of bread for him. The family’s toaster holds only 2 slices of
bread and toasts only 1 side at a time. The person who toasts bread has to
toast one side of a slice of bread, take out the slice, turn it over, and put
it back in the toaster to toast the other side. It takes exactly 1 minute to
toast 1 side of a piece of bread. Dad has figured out how to toast 3 slices on
both sides in only 3 minutes. How does he do it?
First minute: Dad
toasts Dan’s bread on side 1 and Ed’s bread on side 1. Then he removes Dan’s
slice, turns it around, and puts it back in the toaster. He puts Ed’s slice
aside and puts Frank’s bread in the toaster.
Second minute: Dad toasts Dan’s bread on side 2 and Frank’s bread on side 1. He removes both slices, turns Frank’s around, and puts it back in the toaster. He gives Dan his toast and puts Ed’s slice back in the toaster.
Third minute: Dad toasts Frank’s slice on side 2 and Ed’s slice on side 2. Then he serves those slices to Frank and Ed.
Second minute: Dad toasts Dan’s bread on side 2 and Frank’s bread on side 1. He removes both slices, turns Frank’s around, and puts it back in the toaster. He gives Dan his toast and puts Ed’s slice back in the toaster.
Third minute: Dad toasts Frank’s slice on side 2 and Ed’s slice on side 2. Then he serves those slices to Frank and Ed.
Reasoning
136. True or False?
Read the following
statement in capital letters and think about whether it is true or false.
THIS
STATEMENT IS FALSE.
What
do you think? Explain what makes this statement so confusing.
If the statement is
true, then it must be false; but if it's false, then it's true! The word for
such a statement that contradicts itself
is paradox. By the way, this is probably the only statement you can make that is neither true nor false.
is paradox. By the way, this is probably the only statement you can make that is neither true nor false.
Spatial Awareness
137. A Penny Apiece
Cut a big circle out
of a sheet of paper. Place seven pennies on the paper circle as follows:
1.
Place
six pennies, evenly spaced, around the outer edge of the circle. Label the top
penny "A," and the others, "B," "C,"
"D," "E," and "F," going clockwise around the
circle.
2.
Place
one penny in the middle of the circle. Label it "G."
Now divide the circle
into sections by drawing three straight lines so that there is only one penny
in each section.
Begin by drawing a
horizontal line across the circle, just below penny G.
Next, draw a diagonal line beginning just to
the left of penny A, passing to the right of penny G, and just beneath penny C.
Then draw another diagonal line beginning
just to the right of penny A, passing to the left of penny G, and just beneath
penny E.
Penny G should end up in a small triangle all
by itself.
Source:
Sterling, Math
Tricks, Puzzles & Games, p.45Spatial Awareness
138. Cups Up
Take three paper cups
and put them in a row. Turn the first and third cups upside down, but leave the
middle cup right side up. Your task is to get all the cups right side up, but
you must follow these rules:
You have only three moves.
For each move, you must turn over two cups at
a time—never one at a time.
First move: Turn over
the first and second cups.
Second move: Turn over the first and third cups.
Third move: Turn over the first and second cups.
Now
they should all be right side up.
STRATEGY:
Act it out.
Spatial Awareness
139. Exactly Two
Draw a grid made up of six horizontal squares and six vertical squares.
The
grid will have 36 squares. Place 12 pennies on the grid, one to a square, so
that each of the six horizontals, each of the six verticals, and each of the
two diagonals contains exactly two pennies.
Here are three
solutions. Are there more?Spatial Awareness
140. Pennies on a Grid
In the grid below,
you'll find four Xs in a row and three Xs in a row. (One row of Xs is vertical
and the other is horizontal.) Your challenge is to make 3 rows of 3 Xs by
moving only one X. (Hint: Use pennies so that you can try out different
strategies.)
x


x


x

x

x


x


Move the x in boldface
type to the box marked either a or b.
x

x

x

x

a

x


x

x

x


x


b

Spatial Awareness
141. Two Moves
Can you change two
rows of Xs into a circle by moving only two of the Xs?
Go from
this: X X X
X X X
to this:
X X
X X
X X
by
moving only two Xs.
Hint: Try it by using pennies. But remember, you can move only
two of the pennies. The others stay exactly where they are!
Move the X at the
right in the top row and the X in the middle of the bottom row to the position
of the bottom two Xs in the circle
Spatial Awareness
142. Three Moves
There are 10 letters
in the triangle. Change the triangle so that it points down. Move one letter at
a time. You have only three moves. (Hint: Lay 10 pennies out so that they match
the letters in the triangle. Then you can try out different moves.)
A
B C
D E F
G H I J
Move G so that it is
next to B. Move J so that it is next to C. Switch A from the top to the bottom
of the triangle to make the point.
A
B C
D E F
G H I J
G B C J
D E F
H I
A
Source:
Lowell House, Brain
Games, p. 37Word & Letter Play
143. A?
If you start with the
number one and use only integers (whole numbers), how far do you have to count
before you need to use the letter a in spelling a number?
You have to count up
to one thousand.
Source: Based on a puzzle in More Puzzles for
Pleasure and Leisure by Thomas L. Hirsch. New York: AbelardSchuman, 1974Word & Letter Play
144. A Different Alphabet
Which letter comes
next?
A C F J O
The next letter is U.
The series moves forward by skipping 1 letter of the alphabet and then 2
letters and then 3 and so on.
Source: Cameron, IQ Puzzles, p.9Word & Letter Play
145. A Skinny Riddle
What is being
described in this riddle?
When I am filled,
I can point the way.
When I am empty,
Nothing moves me.
A gloveI can point the way.
When I am empty,
Nothing moves me.
Word & Letter Play
146. A to Z
Use all twentysix
letters of the English alphabet to complete the following 13 words, but use
each letter only once.
·
b
a __ __ a i n
·
l
__ __ g e r
·
d
y __ __ s t y
·
__
__ g o t e
·
s
a __ __ a t i o n
·
d
i __ __ p a n
·
p
u m __ __ i n
·
d
e __ __ a y
·
b
o __ __ a r
·
d
i __ __ i t
·
s
u n __ __ r n
·
o
b l __ __ u e
·
l
i __ __ o f f
·
bargain
·
lodger
·
dynasty
·
zygote
·
salvation
·
dishpan
·
pumpkin
·
deejay
·
boxcar
·
dimwit
·
sunburn
·
oblique
·
liftoff
Source: p. 94 in Big Book of Games II,
New York: Workman, 1988.
Word & Letter Play
147. All in the Family
These words all
belong to the same logical family because they have something in common:
·
footloose
·
committed
·
successful
·
address
·
millennium
Which of the following words belong to the
same family?
·
silly
·
ancestor
·
millstone
·
heedless
Heedless. (All the
words in the family have two pairs of double letters.)Word & Letter Play
148. Alphabet Challenge
Use all twentysix letters of the alphabet to
complete the following eleven words, but use each letter only once in the
course of this puzzle.
To keep track of which letters you use, print
this page and cross off the letters:
A
B C D E F G H I J K L M N O P Q R S T U V W X Y Z
1.
__
a __ z
2.
__
u i e __
3.
__
u __ c a
4.
e
__ t r __
5.
__
i o __ __ n
6.
__
a __ __ f u l
7.
__
r o __ __
8.
__
e __ __ a t
9.
__
__ a l a
10. __
o l a __
11. __
o r c __ p i n e
1.
jazz
2.
quiet
3.
yucca
4.
extra
5.
violin
6.
bashful
7.
grown
8.
defeat
9.
koala
10. molar
11. porcupine
From The Best of Brain Teasers. Westminster, CA: Teacher
Created Materials, Inc., 1999.Word and Letter Play
149. Anagram Rhyme
Will
Shortz, a famous puzzle master, created this one: For each of the following
four words, come up with another English word that uses all THE SAME letters
but in a different order. The four words you come up with will rhyme with one
another.
·
ONSET
·
NEWS
·
WRONG
·
HORNET
·
STONE
·
SEWN
·
GROWN
·
THRONE
STRATEGY:
Look for a pattern in the letters – what is the same in each that could rhyme?
Word & Letter Play
150. X and Y
Finish
each of the following threeword expressions. Some of the expressions are used
as verbs, some as nouns, and some as adjectives.
1.
eat
and
2.
huff
and
3.
mix
and
4.
rise
and
5.
twist
and
6.
slash
and
7.
wash
and
8.
watch
and
9.
bait
and
10.
tar
and
1.
drink
or run
2.
puff
3.
match
4.
fall
or shine
5.
shout
or turn
6.
burn
7.
wear
or dry
8.
wait
9.
switch
10.
feather
Other answers may be possible.
From The
Best of Brain Teasers from Teacher Created Materials, p. 19
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