Juice

1

• Juice
• You buy a bottle of juice for 1.00. The juice
  costs 90 cents more than the empty bottle.
• How much does the empty bottle cost?

2

• Talia's Giveaway   Talia has some money in her
  pocket. She gives half of the money to Allison.
  Then she gives 1/4 of what she has left to
  Lauren. Talia then sees David, and she gives him
  1/3 of what she has left. Now you come along,
  and Talia equally shares the money she has left
  with you. You get 2!
• How much money did Talia have to start with?
• Who gets the most money?

3

• Who Carries the Rocks?
•    April, Rosa, and Carrie, who are sisters, went
  on a hike. They found four rocks that they want
  to bring home to add to their collection. Each
  girl has a backpack to carry the rocks.
• In how many different ways can the three sisters
  take home four rocks in their backpacks?

4

• Pizza Party
•   Roma Pizzeria offers the following toppings for
  a standard large pizza pepperoni, mushrooms,
  peppers, onions, and sausage. In addition to
  ordering a plain pizza, you can order any number
  of toppings, even all five (which happens to be
  the "special").
• How many different kinds of large pizza do you
  have to choose from?

5
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6

• Round and Round  There is a machine with 2 gear
  wheels. One wheel has 8 teeth, and the other
  wheel has 5 teeth. If you turn the large wheel,
  the teeth make the small wheel turn, but in the
  other direction. Suppose you turn the wheels so
  the larger wheel goes around once. The smaller
  wheel is not back in its starting place. So, you
  keep turning the wheels until they both get back
  to their starting places.
• How many times will each wheel go around?

7

• Sticks and Squares   
• Which toothpick can you take away to leave three
  equal squares?

8

• 100 Wins!
•   Use all the numbers shown, any of the following
  four operations, , -, , , and parentheses to
  make a total of 100. 1 2 3 4 5 6 7 8 9
• You may not change the order of the numbers, or
  use them more than once!

9

• Penny Candy
•   Sonia spent 70 buying small sweets at the
  corner store. She bought some 1 sweets, some 2
  sweets, some 3 sweets, some 5 sweets, and some
  10 sweets. She bought 17 sweets altogether, four
  each of two kinds, three each of the other three
  kinds.How many candies did she buy at each
  price?

10

• Doubling Amoebas
•   Amoebas are one-celled animals that reproduce
  by dividing in two. One amoeba becomes two, two
  become four, and so on. If they have enough food,
  amoebas can double their population every 24
  hours.
• If you start with just one amoeba in a jar of
  pond water at 10 A.M. on Monday morning, how many
  amoebas are in the jar by Wednesday of the next
  week at 10 A.M.? (Assume that none die.)

11

• To Get to the Other Side
• Zoe, Claire, and Kristin have to cross a river
  to visit their friend Tasha. They have a boat,
  but they also have a problem. Zoe and Claire
  each weigh 50 kg. Kristin weighs 75 kg, and the
  boat will carry only 100 kg at a time. Oh no! We
  can't all get across the river! moans Claire.
• Kristin thinks for a moment and says, I know a
  way we can all get across. It will just take more
  than one trip.
• What is Kristin's plan?

12

• The Bridge
• A Family of four (father, mother, son, and
  daughter) went on a hike. They walked all day
  long and, when evening was already drawing on,
  came to an old bridge over a deep gully. It was
  very dark and they had only one lantern with
  them. The bridge was so narrow and shaky that it
  could hold no more than two persons at a time.
  Suppose it takes the son 1 minute to cross the
  bridge, the daughter 3 minutes, the father 8
  minutes, and the mother 10 minutes.
• Can the entire family cross the bridge in 20
  minutes? If so how? (When any two persons cross
  the bridge, their speed is equal to that of the
  slower one. Also the lantern must be used while
  crossing the bridge.)

13

• Ducky numbers.
• For many years now Baron Münchhausen has gone to
  a lake every day to hunt ducks. Starting on
  August 1, 2000, he says to his cook "Today I
  shot more ducks than two days ago, but fewer than
  a week ago."
• For how many days can the baron say this?
  (Remember, the baron never lies.)

14

• Musketeering swordplay.
• At the royal fencing competition in France, the
  first four places were taken by Athos, Porthos,
  Aramis, and D'Artagnan. The sum of the places
  taken by Athos, Porthos, and D'Artagnan was 6.
  The sum of the places taken by Porthos and Aramis
  was also 6.
• What was the place taken by each of the
  musketeers if Porthos ranked higher than Athos?

15

• Be fruitful and multiply.
• One day all of Mrs. Brown's grandchildren came
  to visit her. There was a bowl of apples and
  pears on the kitchen table. Mrs. Brown gave each
  child the same number of pieces of fruit without
  keeping track of which kind. Bobby got 1/8 of all
  the apples and 1/10 of all the pears.
• How many grandchildren did Mrs. Brown have?

16

• Returnable bottles.
• A government program allows people to collect
  empty milk bottles and exchange them for bottles
  full of milk. Four empty bottles may be exchanged
  for one full bottle. How many bottles of milk can
  a family drink if it has collected 24 empty
  bottles?

17

• Bottles Solution
• Its not hard to see that the family can drink 6
  1 7 bottles of milk, and it will have three
  empty bottles left. Then the family can borrow
  one empty bottle, exchange the four empty bottles
  for one bottle of milk, drink it, and return the
  bottle it borrowed. Thus, the family can drink
  eight bottles of milk.

18

• Valentines Cards
• Brrr! It's been so cold where we live in the
  Midwest that yesterday the schools were closed!
  Fortunately for their parents I was able to take
  care of my nephews, Barney and Danny, and their
  cousin, Gina. We had lots of fun doing puzzles,
  playing games, and reading books, but by early
  afternoon the boys were ready to watch a video
  and Gina wanted to make valentines. I set up a
  valentine making station on the kitchen table,
  complete with red and pink paper, doilies,
  stickers, markers, glue, glitter and other things
  I had been saving for just such an occasion.
  After the video was over, the boys wanted to see
  Ginas valentine creations. 
• "Not until you guess how many I made," said Gina,
  holding her cards behind her back.
• "It would be more fun if you gave us some clues,
  Gina," suggested Barney. "Then we wouldnt have
  to guess. We could figure it out."  
• Always up for a challenge, Gina left the room and
  soon returned, ready with her clues.
• "OK, now listen, Barney. If I give half my
  valentines to my best friends at school, and then
  I give half of what is left over to my friends in
  my apartment building, I will still have enough
  valentines left over to give you, Danny, Aunty
  and Uncle Bill a valentine."

19

• Christmas Presents
• 3 children, Danny, Gina and Barney, helped wrap
  the Christmas presents.
• "We wrapped 30 presents altogether," Danny said.
• "Danny and I wrapped half the presents, Gina
  added.
• "Danny and I wrapped 4/5ths of the presents,
  boasted Barney, and Gina and I wrapped 7/10ths
  of the presents! "
• Can you get this challenge "wrapped up?" How
  many presents did each child wrap?

20

• The Quilt
• How many squares did you say you had in this
  quilt, Gina?" asked Danny"Sixteen. I counted
  them all so I know, its sixteen," said Gina.
• "Well, I hate to be one to disagree, but I think
  you have more than sixteen squares on that
  quilt!" said Barney, winking, "And I'll bet Aunty
  will agree with me!What do you think? Are
  there more than 16 squares on Gina's doll quilt?
  If so, how many squares can you find?

21
The Parade We saw 7 clowns in the parade. All
were riding vehicles. Some clowns were riding
bicycles and the rest were riding tricycles
(3-wheeled bikes). There were 17 wheels in
all," How many bicycles were the clowns
riding?"
22

• New Shoes 
• One day, two mothers and two daughters went
  shopping for shoes. Their shopping spree was
  successful each bought a pair of shoes, and all
  together, they had three pairs.
• How is this possible?

23

• Athletes in Place  
• Five athletes were returning from a
  cross-country race. Athlete C placed third, and
  athlete E placed second. From the following
  information, can you tell how athletes A, B, and
  D placed in the race? Athlete A was not last.
  Athlete A came in after E. Athlete D was not
  first.

24

• Dogs on Trial 
• Someone's dog goes around the neighborhood every
  night getting into people's garbage pails and
  making a mess. Some of the neighborhood kids say
  they know what the guilty dog looks like, but the
  culprit strikes at night, so it's hard to see.
  Each of the four witnesses has one and only one
  detail right, and each detail is described
  correctly by only one witness.
• Dan says the dog is white, fluffy, wears a red
  collar, and has a long tail.Karen says the dog
  is black, has short hair, wears a red collar, and
  has a long tail.Max says the dog is brown, has
  long, silky hair, wears a blue collar, and has a
  long tail.Emma says the dog is spotted, fluffy,
  wears a red collar, and has a short tail.
• Can you correctly describe the guilty pooch?
•  

25
Dogs on Trial- Solution

• The dog is white, has short hair, wears a blue
  collar, and has a short tail. To arrive at the
  answer, begin by making a chart like the
  following
•  Next, cross out the details in each column that
  are repeated. (only one detail is described
  correctly by each witness the dog can't be
  fluffy, can't wear a red collar, and can't have a
  long tail.) Now you have all the information you
  need
• The dog wears a blue collar and has a short tail.
  
• The dog must be white, because Dan is wrong about
  the hair, the collar, and the tail, and he has to
  be right about one detail.
• Karen, Max, and Emma are wrong about the dog's
  color therefore the dog must have short hair,
  because Emma has to be right about one detail.

26

• 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 Value of Months   If March 43 and May 39,
  then by the same logic, what does July equal?

27

• 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."
• How were George and Dan related?

28

• Which Way? 
• Once a boy was walking down the road, and came
  to a place where the road divided in two, each
  separate road forking off in a different
  direction.
• A girl was standing at the fork in the road. The
  boy knew that one road led to Lieville, a town
  where everyone always lied, and the other led to
  Trueville, a town where everyone always told the
  truth. He also knew that the girl came from one
  of those towns, but he didn't know which one.
• Can you think of a question the boy could ask
  the girl to find out the way to Trueville?

29

• 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
  timenever one at a time.

30

• 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.

31

• A Pocket Full of Coins 
• Janice has 7.56 worth of coins in her pocket.
  The coins are of four different denominations,
  and she has the same number of each denomination.
  What are the four denominations, and how many
  of each does she have?

32

• Average Speed  Louise runs the first half of a
  race at 5 miles per hour. Then she picks up her
  pace and runs the last half of the race at 10
  miles per hour. What is her average speed on the
  course? 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?

33

• Who Rocked the Boat?  
• Three boats one red, one blue, and one yellow
  were out on the river this morning. By reading
  the following clues, can you tell the color and
  type of each boat, who is on each boat, and which
  country the people come from? Write your answers
  on a chart like this oneThe woman is not in a
  yellow boat and is not from France.
• The red boat is not from Italy.
• The kids are in a blue boat, but they are not
  from Italy or Sweden.
• The man and his dog are on a yacht with an
  Italian flag.
• The sailboat is from France, while the canoe is
  red.

34
Fill in the Missing Square 

• Can you fill in the missing square with the
  number that logically belongs there?
•  

35

• Where's the Fruit Juice? 
• A catering company sells large containers of
  apple juice and large containers of orange juice.
  Right now the company has six containers, each
  holding the following amounts
• Container A 30 litresContainer B 32
  litresContainer C 36 litresContainer D 38
  litresContainer E 40 litresContainer F 62
  litres
• Five of the containers hold apple juice, and one
  container holds orange juice.
• Two customers come into the shop. The first
  customer buys two containers of apple juice. The
  second customer buys twice as much apple juice as
  the first customer.
• Which container is holding the orange juice?

36

• 5 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.
• List the dogs in the order of their weights,
  starting with the heaviest.

37

• How Many Students?  A new school has opened with
  fewer than 500 students. One-third of the
  students is a whole number. So are one-fourth,
  one-fifth, and one-seventh of the students. How
  many students go to this school?
• How Many Coins?  A bag holds 50 coins that add up
  to 1.00. How many coins of each denomination
  (value) are in the bag?

38

• 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?

39

• More 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 euro. 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 cent
  for 2 pieces.
• How many pieces of each price candy did Alice
  buy?

40
On a distant island live three types of humans -
Knights, Knaves and Normals. The Knights always
tell the truth, the Knaves always lie, and the
Normals sometimes lie and sometimes tell the
truth. Detectives questioned three inhabitants
of the island - Al, Bob, and Clark - as part of
the investigation of a terrible crime. The
investigators knew that one of the three
committed the crime, but did not at first know
which one. They also knew that the criminal was a
Knight, and that the other two were not. How they
knew these things is not important for the
solution. Additionally, the investigators made a
transcript of the statements made by each of the
three men. What follows is that transcript Al
I am innocent. Bob That is true. Clark Bob
is not a Normal. After carefully and logically
analyzing their information, the investigators
positively identified the guilty man. Was it Al,
Bob or Clark?
41

• Chewing GumSome problems have a solution that
  is easy to find, but the best solution is hard to
  find. The purpose for this homework is to look
  for the best solutions. There are 10 gumball
  machines. Most of the machines have gumballs that
  weigh 1 gram, but one of the machines has
  gumballs that weight 1.2 grams. You can't tell
  the difference between them just by holding them.
  You need to use a scale. You can take as many
  gumballs out of the machines as you need. How can
  you determine which machine has the heavier
  gumballs while using the scale as few times as
  possible?

42

• Marbles 1
• This time you have a balance instead of a scale.
  The way a balance works is that you place items
  in each side, and the balance will tilt toward
  whichever side is heavier. You have 8 marbles.
  Most of them have the same weight, but one marble
  is slightly heavier than the others. Again, you
  can't tell the difference just by holding them.
  There is a way you can tell which is the heavy
  marble while using the balance only twice. How?

43

• Marbles2
• Now you have 12 marbles. Most of them have the
  same weight, but one marble is slightly
  different. You don't know if the different marble
  is heavier or lighter than the others. How can
  you tell which is the different marble while
  using the balance only three times?