Fill the 5 litre container and empty it into the 9 litre one. Fill the 5 litre (again) and empty 4 litres into the 9 litre container. Now - empty the remaining litre into the 6 litre container. Finally re-fill the 5 litre container and empty into the 6 litre one - and you're done.
First fill 5 litre and pour it into 7 Litre. Then again fill 5 litre and pour to 7 litre. Now 3 litres are left in 5 litre container. Empty 7 litre and pour 3 litre in it. Again fill 5 litre and pour in 7 litre. Now 7 litre is full and 1 liter left in 5 liter container. Empty 7 litre and pour 1 litre which is left in 5 litre container. Now 1 litre is already in 7 litre container, now fill 5 litre and pour into 7 litre container. now it is 6 litre in 7 litre container. DONE!
Here's how to proceed:Fill container B with 3 liters.Pour the 3 liters from container B into container A.Fill container B again with 3 liters.Carefully pour from container B into container A, until container A is full.Container A already had 3 liters, so it only takes 2 more liters to fill it to 5 liters, leaving 1 liter remaining in container B.
Several ways to achieve this - here is one solution. Fill the 5 litre container and pour it all into the 9 litre container. Fill the 5 litre container and pour it into the 9 litre container until the latter is full - leaving 1 litre in the 5 litre container. Empty the 9 litre container. Fill the 3 litre container and empty into 9 litre container. Repeat. There are now 6 litres in the 9 litre container. Pour the 1 litre from the 5 litre container into the 9 litre container which now contains 7 litres.
This method works with any such problem, as long as the two buckets' liter-capacities (or gallon capacities, etc.) have no common factors, or else the common factors are also factors of the amount you're trying to measure. Fill the 7-liter bucket, and empty 5 liters of it into the 5-liter bucket; then dump out the 5 liters. Two liters will remain in the 7-liter bucket; transfer them to the 5-liter bucket. Fill the 7-liter bucket again, and empty enough of the bucket into the 5-liter bucket to fill it. That should only be 3 liters transfered, leaving 4 liters left in the 7-liter bucket. QED.
1)Transfer 7 liters from the 12-liter jar into the 7-liter jar.We now have 5 liters in the 12-liter jar and 7 liters in the 7-liter jar. The 5-liter jar is empty, as of now.2)Transfer 5 liters from the 7-liter jar into the 5-liter jar.The 12-liter, 7-liter, 5-liter jars now contain 5, 2 and 5 liters respectively.3)Empty the contents of the 5-liter jar into the 12-liter jar.The 12, 7, 5- liter jars now contain 10, 2 and 0 liters respectively.4)From the 7-liter jar, take out 5 liters and pour 7 liters from the 12-liter jar into the 7-liter jar.We now have 3 liters in the 12-liter jar and 7 in the 7-liter one, while the 5-liter jar has only two liters in it.5)Fill up the remainder of the 5-liter jar using the 7-liter jar.That leaves us with 3 liters on the 12-liter jar and 4 liters in the 7-liter jar. The 5-liter jar is full.6)Pour the contents of the 5-liter jar into the 12-liter jar.There are 8 liters in the 12-liter jar and 4 liters in the 7-liter jar, while the 5-liter jar is empty.7)Pour the 4 liters that are in the 7-liter jar into the 5-liter jar.We now have 8 liters in the 12-liter jar and 4 liters in the 5-liter jar. The 7-liter jar is empty.8)Fill the 7-liter jar using the 12-liter jar.There is now only 1 liter in the 12-liter jar and 7 liters in the 7-liter jar and 4 liters in the 5-liter jar.9)Fill up the 5-liter jar using the 7-liter jar.There is now 1 liter in the 12-liter jar and 6 liters in the 7-liter jar and 5 in the 5-liter jar.NOTE: This might not be the only way, or the shortest way to do it.
There is most likely a more efficient way to do this, but this is the best I can do for now.Notation: ( x , y ) where x is the amount of water in the 5-liter container and y is the amount of water in the 7-liter container1. Fill the five-liter container ( 5 , 0 )2. Pour the five-liter container into the seven-liter container ( 0 , 5 )3. Fill the five-liter container ( 5 , 5 )4. Fill the seven-liter container with the five-liter container, leaving 3 liters in the five-liter container ( 3 , 7 )5. Pour out the seven-liter container ( 3 , 0 )6. Pour the five-liter container into the seven-liter container ( 0 , 3 )7. Fill the five-liter container ( 5 , 3 )8. Fill the seven-liter container with the five-liter container, leaving 1 liter in the five-liter container ( 1 , 7 )9. Pour out the seven-liter container ( 1 , 0 )10. Pour the five-liter container into the seven-liter container ( 0 , 1 )11. Fill the five-liter container ( 5 , 1 )12. Pour the five-liter container into the seven-liter container ( 0 , 6 )
Notes: There is most likely a more efficient way to do this, but this is the best I can do for now.Notation: ( x , y ) where x is the amount of water in the 5-liter container and y is the amount of water in the 7-liter container1. Fill the five-liter container ( 5 , 0 )2. Pour the five-liter container into the seven-liter container ( 0 , 5 )3. Fill the five-liter container ( 5 , 5 )4. Fill the seven-liter container with the five-liter container, leaving 3 liters in the five-liter container ( 3 , 7 )5. Pour out the seven-liter container ( 3 , 0 )6. Pour the five-liter container into the seven-liter container ( 0 , 3 )7. Fill the five-liter container ( 5 , 3 )8. Fill the seven-liter container with the five-liter container, leaving 1 liter in the five-liter container ( 1 , 7 )9. Pour out the seven-liter container ( 1 , 0 )10. Pour the five-liter container into the seven-liter container ( 0 , 1 )11. Fill the five-liter container ( 5 , 1 )12. Pour the five-liter container into the seven-liter container ( 0 , 6 )
Fill the 5 liter container.Pour it into the 8 liter container.Fill the 5 liter container again.Pour it into the 8 liter container again, but stop when the 8 liter container is full.The 5 liter container now contains 2 liters.
-- Fill the 3 from the hose.-- Pour the 3 into the 5. The 5 container now has unfilled capacity of 2.-- Fill the 3 again from the hose.-- Pour the 3 slowly into the 5. It'll take only 2 to fill the 5 container.-- There is now 1 remaining in the 3 container. QED
As illustrated in the 1995 movie Die Hard 3 (Bruce Willis, Samuel K. Jackson), you can measure out exactly 7 liters in the following manner:Fill the 5 liter container, then use that 5 liters to fill the 3 liter container.Dump out the 3 liter container.What was left in the 5 gallon container is 2 liters. Pour this into the 3 liter container.Fill the 5 liter container again.You now have 7 liters : 5 in the large container and 2 in the smaller one.
You have to have something else to build the 4 liters into. Call it The Tub.Fill the 5.Pour the 5 into the 3.That leaves 2 liters in the 5.Pour them into The Tub. You now have 2 liters in The Tub.Empty the 3.Fill the 5.Pour the 5 into the 3.That leaves 2 liters in the 5.Pour them into The Tub. You now have 4 liters in The Tub.QEDYou do not have a TUB, it is not in the problem.Fill the 5 liter containerPour it into the 3 liter container leaving 2 liters in the 5 liter containerEmpty the 3 liter containerPour the 2 liters from the 5 liter container into the 3 liter containerFill the 5 liter containerFill the remainder of the 3 liter container from the 5 liter containerSince the 3 liter container already had 2 liters in it, one liter from the 5 liter container will fill it leaving 4 liters in the 5 liter container.Solved
You would need 5 bottles of 500 ml each to fill a 2.5-liter container.
# Fill the 5 liter bucket # Pour it into the 7 liter bucket # Fill the 5 liter bucket # Fill the 7 liter bucket from the 5 (2 liters go in leaving 3 liters in the 5 liter bucket) # Empty the 7 liter bucket # Pour the 3 liters from the 5 liter bucket into the 7 liter bucket # Fill the 5 liter bucket # Fill the 7 liter bucket from the 5 liter bucket (4 liters go in leaving 1 liter in the 5 liter bucket) # Empty the 7 liter bucket # Pour the 1 liter form the 5 liter bucket into the 7 liter bucket # fill the 5 liter bucket. You now have 5 liters in the 5 liter bucket and 1 liter in the 7 liter bucket; 6 liters in all. Pour the 5 liters into the 7 liter bucket if you want all 6 liters in one container.
First fill 5 litre and pour it into 7 Litre. Then again fill 5 litre and pour to 7 litre. Now 3 litres are left in 5 litre container. Empty 7 litre and pour 3 litre in it. Again fill 5 litre and pour in 7 litre. Now 7 litre is full and 1 liter left in 5 liter container. Empty 7 litre and pour 1 litre which is left in 5 litre container. Now 1 litre is already in 7 litre container, now fill 5 litre and pour into 7 litre container. now it is 6 litre in 7 litre container. DONE!
Here's how to proceed:Fill container B with 3 liters.Pour the 3 liters from container B into container A.Fill container B again with 3 liters.Carefully pour from container B into container A, until container A is full.Container A already had 3 liters, so it only takes 2 more liters to fill it to 5 liters, leaving 1 liter remaining in container B.
Fill small 3 liter jug with water. Pour into large 8 liter jug. Repeat. Now 6 liters of water in large jug. Repeat again but stop when large jug full. Leaves 1 liter in small jug. Empty large jug. Pour water from small jug into large jug. Refill small jug and pour into large jug. There are now 4 liters of water in large jug.
Fill the 5 litre and empty into the 12 litres twice. Then fill it again and with this pour to the brim of the 12 litres. You are then left with 3 litres in the 5 litre jug. Because: 5+5+5=15, however you have only space for 12. i.e. 15-12 is 3