1. An eight gallon container is full and both a three gallon container and a five
gallon container are empty. Without using any other containers, divide the water into two
equal amounts.
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Answer
18 |
2. You go to a tap that delivers an unlimited amount of water.
You have two empty containers, one of 7 liters, the other of 11 liters. At each operation
one container must be completely filled or completely emptied. How many operations are
required to fill one of the containers with exactly 6 liters of water?
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Answer
18 |
3. Given four containers: 2, 4, 5, 9, with the 9 container full.
Divide the liquid into three equal portions (without spilling any) in the fewest
steps.
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Answer
18 |
4. You have two containers; one holds eight gallons, the other
holds five. You can have as much water as you want. Your task: measure exactly four
gallons of water into the five-gallon container.
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Answer
18 |
5. You have two containers; one holds five gallons, the other
holds three. You can have as much water as you want. Your task: measure exactly four
gallons of water into the five-gallon container.
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Answer
19 |
6. You have two empty containers. A 10 liter container and a 7
liter container. You have a unlimited supply of water and you are allowed to empty the
containers. Can you measure 9 liter in one of the two containers?
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Answer
19 |
| 7. A
mother has three sick children. She has a 24-ounce bottle of medicine and needs to give
each child eight ounces of the medicine. She is unable to get to the store but has
containers that measure 5, 11 and 13 ounces. How can she divide the medicine to give each
child an equal portion? |
Answer
19 |
8. Classes were finished for the day at the Pithuan University.
Aploob, Breemitz, Chilzook, Doipus, and Erzgt headed for the local bar to have some
spoozle (the beverage with the taste of peppermint lemonade mixed with beer). As was
custom, they each brought their own mugs. Each mug had a different capacity: 6, 5, 4, 3,
and 2 eezfs (a eezf is a liquid measure used on the planet Pith). Being students, they
didn't have much money, so they had the bartender fill the 5, 3, and 2 eezf mugs to the
brim and decided to share in the standard Pithuan manner. Doipus poured all the spoozle he
could from his mug into another mug. One of the students then pointed out that he didn't
have any spoozle in his mug. Next, Aploob poured all the spoozle he could from his mug
into another mug. The same student complained that he still didn't have any spoozle. Then
Erzgt poured all the spoozle he could from his mug into another mug. The complaining
student was getting annoyed, and pointed out that he better get some spoozle soon. Aploob
tried again by pouring all the spoozle he could from his mug into another mug. The
complaining student was really upset and said he would leave if he didn't get any spoozle.
Breemitz explained that they were just teasing him and poured all the spoozle he could
from his mug into the complainer's mug. Finally everyone had some spoozle, and amazingly
enough, exactly the same amount. As always, no one drank or spilled any spoozle until the
transfers were complete. Which mug belonged to which student, who was the complainer, and
what are the details of the transfers?
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Answer
18 |
9. You have two containers; one holds seven gallons, the other
holds nine gallons. You can have as much water as you want. Your task: measure exactly 10
gallons of water devided into both containers, when you start with container 7 full and
when you start with container 9 full.
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Answer
Answer
18 |
10. You have three boxes; one hold 6 apples, the second holds 9
apples, and the third 21 apples. Your task: to move the apples in two and three moves to
get exactly 12 apples in each box. One move consists of doubling the number of apples of
the receiving box.
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Answer
19 |
11. You
have a 12 liter container of wine and you want to give your friend 6 liters. Your friend
has only a 5 liter contaner and an eight liter container. How can you give your friend 6
liters without spoiling a drop?
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Answer
18 |
12. You go to a tap that delivers an unlimited amount of water.
You have two empty containers, one of 5 liters, the other of 3 liters. At each operation
one container must be completely filled or completely emptied. How many operations are
required to fill one of the containers with exactly 4 liters of water?
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Answer
18 |
13. You go to a tap that delivers an unlimited amount of water.
You have two empty containers, one of 4 liters, the other of 9 liters. How many operations
are required to fill one of the containers with exactly 6 liters of water?
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Answer
18 |
14. Len looked up from what he was reading. "Here's is a
teaser about a pharmacist who has a 24-ounce jar of medicine but only three measures that
are not broken. Two 13-ounce and 5-ounce," he said. "He has to supply 12 ounces
of it." "That's easy," Ann told him. "He divides the 24 ounces by eye
between the two 13-ounce measures." "I didn't finish," replied Len.
"That's no good, because those two measures are quite different shapes." It
could be done, however, and with only the containers mentioned.
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Answer
19 |
15. You have two cylindrical glasses of the same height. The
first can hold 21 centilitre water, the other 9 centilitre water. Using an ordinary tap
and those two glasses, how can you fill the biggest glass with 20 centilitre of water?
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Answer
19 |
16. A woman has three children who are ill. She goes out to the
chemist and comes back with a 24 cl bottle of medicine, of which she has to give exactly
8cl to each child. When she comes home she sees that the chemist didn't put a 8cl
measuring spoon with it. He did put two other spoons in the bag, one of 5cl and one of 13
cl. She thinks for a while and than within seven measurings using the two awkward spoons,
she managed to give each of her children exactly 8cl of medicine. Do you know how she did
it?
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Answer
19 |
17. "There you are, Ted," his mother said. "Two
pitchers, both full with milk. One holds a pint and a half, the other two and a half
pints." "Okay, Mom." The boy was bored doing nothing. "What must I do
with them?" "There are two clean jugs in the closet," his mother told
him." One holds a quart, and the other a pint. I want you to divide the milk among
the four, so ther'll be a pint in each. And don't use anything else." What are the
least number of transfers needed to do the job?
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Answer
18 |
18. Abby, Betty, and Clarence were at the dairy on a school
fieldtrip. The dairyman had two ten-gallon containers full of milk. Abby had a three pint
bottle, Betty had a four pint bottle, and Clarence had a five pint bottle. The dairyman
offered to put two pints of milk into each of the three children's bottles if they could
measure it out exactly using only the unmarked containers and without wasting any milk.
Clarence, a puzzle enthusiast, claimed he could do it in exactly eight transfers. How?
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Answer
18 |
19. You have a 5 liter container and a 3 liter container. The
objective is to fill the 5 liter container with exactly 4 liters. You are not allowed to
pour water from one container to the other more than 2 times. (e.g. fill the 3 liter and
pour into the 5 liter = once. Fill the 3 liter again and pour into the 5 liter = twice -
no more "pourings" allowed). How do you do it?
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Answer
18 |
20. You have 4 jugs, two of them being full 10 Litre jugs, one an empty 5 Litre jug and the
last one an empty 4 Litre jug. There are no markings on them, no measuring instruments, etc (so you can only pour until one is full or empty).
You cannot get rid of any water, ie you can only pour. How do you end up with exactly 3 Litres in both the small jugs in minimum steps?
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Answer
18 |
21. Given a one-liter bottle of wine, three half-liter glasses, and a large shot
glass that holds exactly 3/16 of a liter, divide the liter of wine into four equal parts (one-quarter of a liter in each half-liter glass and the rest in
the bottle).
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Answer
18 |
22. A mother gave her four children a 16 ounce jug of lemonade to take on a
hike. The cap on the jug held exactly 3 ounces. She gave the following challenge to her children, "One of you can drink from the jug, and the
others can drink from cups. Here are four cups. The cups contain 6, 9, 11, and 14 ounces. You may only take three of the cups with you. Before you
start drinking the lemonade, you must divide it equally between your three cups and the jug. You may use the cap on the jug to help you divide the
lemonade. Which cups should you take with you in order to divide the lemonade with the minimum number of transfers?".
Give the answer to the mother's question and the minimum transfers required.
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Answer
18 |
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