[rookie1ja]

Pouring water II. - Back to the Water and Weighing Puzzles
Given three bowls: 8, 5 and 3 liters capacity, divide 8 liters in half (4 + 4 liters) with the minimum number of water transfers. Note that the 8-liter bowl is initially filled with 8 liters of water and the other two bowls are empty - that is all water you have.

Spoiler for Solution:

Pouring Water II. - solution
1. pour 5 litres from the 8-litre to the 5-litre bowl,
2. pour 3 litres from the 5-litre to the 3-litre bowl,
3. pour these 3 litres back to the 8-litre bowl,
4. pour the remaining 2 litres from the 5-litre to the 3-litre bowl,
5. pour 5 litres from the 8-litre to the 5-litre bowl,
6. pour the missing 1 litre from the 5-litre to the 3-litre bowl (there should be 4 litres left in the 5-litre bowl),
7. pour the 3 litres back from the 3-litre to the 8-litre bowl (and that’s it – in 8-litre bowl 4 litres).

[tonycurcio]

Why isn't "pour 4 litres from bowl 8 to bowl 5" a solution?

[larryhl]

Quote

Why isn't "pour 4 litres from bowl 8 to bowl 5" a solution?

because you can't be sure that you're pouring 4 liters into the 5th bowl. it might be 3.5 liters or 4.5 liters. using the solution is the only way to be sure that there are 4 liters in each.

[Domhnall]

Quote

1. pour 5 litres from the 8-litre to the 5-litre bowl,
2. pour 3 litres from the 5-litre to the 3-litre bowl,
3. pour these 3 litres back to the 8-litre bowl,
4. pour the remaining 2 litres from the 5-litre to the 3-litre bowl,
5. pour 5 litres from the 8-litre to the 5-litre bowl,
6. pour the missing 1 litre from the 5-litre to the 3-litre bowl (there should be 4 litres left in the 5-litre bowl),
7. pour the 3 litres back from the 3-litre to the 8-litre bowl (and that’s it – in 8-litre bowl 4 litres).

you have to completly fill the bowl you are pouring into or completly empty the one you are pouring.

[LQEngineer]

1. Fill 5 liter container and empty into 3 liter cup
2. Empty 3 liter cup and transfer remaining 2 liter in the 5 liter container into empty 3 liter cup
3. Fill 5 liter container and empty 1 liter into the 3 liter cup containing 2 liters from step 2.
4. Transfer the remaining 4 liters from 5 liter container into 8 liter empty container
5. Fill 5 liter container and empty into 3 liter cup leaving 2 liters in the 5 liter container
6. Empty the 3 liter container and replace with the remaining 2 liters from 5 liter container
7. Fill 5 liter contain and pour into the 3 liter cup currently containing 2 liters (leaving a balance of 4 liters in 5 liter container)
8. Empty 3 liter container.
This leaves four liters in both the 8 liter and 5 liter containers and zero in the 3 liter container.

[PowerWielder]

It requires 7 pours. Starting with 8L bowl full, this is what each bowl will have at each step. No water being added or removed from original 8L of water.

8L 5L 3L

8 0 0
3 5 0
3 2 3
6 2 0
6 0 2
1 5 2
1 4 3
4 4 0

[malonej7]

* Ignore below. I missed the stipulation that you could only use 8 liters of water. I used the same assumption from the 1st one that we had unlimited access to water.

Here's an alternate solution. It has more steps (I combined a couple steps below), so obviously it is not the correct solution, but I worked it out so I figured I'd post it.

1. Pour 6 liters into 8 liter bowl using the 3 liter bowl twice. (6,0,0)
2. Fill the 5 liter bowl with the water in the 8 liter bowl. (1,5,0)
3. Empty the 5 liter bowl and pour the 1 liter into it from the 8 liter bowl. (0,1,0)
4. Pour 3 liters into the 5 liter bowl from the 3 liter bowl. (0,4,0)
5. Fill the 3 liter bowl 3 different times, emptying it into the 8 liter bowl each time. (8,4,1)
6. Empty the 8 liter bowl and put the 1 liter from the 3 liter bowl into it. (1,4,0)
7. Fill the 3 liter bowl up and empty it into the 8 liter bowl, leaving you with 4 liters in it. (4,4,0)

[hokahey]

Solution:

1. Pour 3L H2O from 8L bowl into 3L bowl
2. Pour 3L H2O into 5L bowl from 3L bowl
3. Pour 3L H2O from 8L bowl into 3L bowl
4. Pour 2L H2O from 3L bowl into 5L bowl (5L bowl now full & 1L still in 3L bowl)
5. Pour 5L H2O into 8L bowl
6. Pour 1L H2O from 3L bowl into 5L bowl
7. Pour 3L H2O from 8L bowl into 3L bowl
8. Pour 3L H2O into 5L bowl from 3L bowl = 4L in 5L and 4L in 8L

[horonym]

This can be done in one pour if the bowls are symetrical.

- pour from the 8L bowl into the 5L bowl until the water reaches the top-edge of the bottom (very hard to explain, but try it in a glass or bowl to see). This will be exactly half of the volumn of the bowl and therefor = 4L.

[Buddyru]

rookie1ja, on Mar 30 2007, 07:13 PM, said:

Pouring water II. - Back to the Water and Weighing Puzzles
Having three bowls: 8, 5 and 3 litres capacity. Share 8 litres in halves (4 + 4 litres) pouring water the minimum times.

8 pours... not the best, but close.

Spoiler for Solution:

8 0 0 START
5 0 3 Pour 3 from 8 into 3
5 3 0 Pour 3 from 3 into 5
2 3 3 Pour 3 from 8 into 3
2 5 1 Pour 2 from 3 into 5
7 0 1 Pour 5 from 5 into 8
7 1 0 Pour 3 from 8 into 3
4 1 3 Pour 3 from 3 into 5
4 4 0 Pour 3 from 3 into 5