Q: How do you fill a 6 liter container unmarked from a 5 liter and 9 liter container?

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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.

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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

Fill the 3-liter bottle to the top, then pour the water into the 5-liter bottle. Refill the 3-liter bottle again and pour water into the 5-liter bottle until it's full. This leaves exactly 1 liter in the 3-liter bottle. Empty the 5-liter bottle, then pour the remaining 1 liter from the 3-liter bottle into the 5-liter bottle. Fill the 3-liter bottle once more and pour it into the 5-liter bottle, making a total of 4 liters.

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 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

== == == == Fill the 3l and dump into 5l. Fill 3l again pour into 5l til full, you now have 1l left in 3 l container. dump 5 onto ground, pour the 1l from the 3l container into the 5l, then fill 3l and dump into the 5l....Presto exactly 4 liters are contained in the 5l container. ALTERNATIVELY (i) Fill the 5l and then fill 3l from 5l. This leaves 2l in the 5l. (ii) Empty 3l (iii) Pour the 2l from the 5l into the 3l. This leaves 1l of spare capacity in the 3l. (iv) Fill the 5l again (v) Fill the 3l from the 5l. This leaves 4l in the 5l.ALTERNATE 2:If flow is steady, time may be used to help. Take amount of time it takes to fill 5 liter bucket, divide by 5 then multiply by 4. Answer will be how long you must let the water flow into the 5 liter bucket to fill it upto 4 liters.