Pouring & Dividing



The containers are shaped so irregularly that you can't measure the
required amount other than by making use of the other containers .
~~~'***'~~~

 
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.

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?

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.

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.

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.

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?

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?

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.

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.

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?

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?

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?

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.

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?

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?

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?

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?

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?


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?


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).


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.



Answer

18

All items Copyright by the respective authors, All Rights Reserved.

Back