### Pouring Puzzle

You have 3 containers, labelled A, B and C.

Container A has a capacity of 8 litres; container B has a capacity of 5 litres; container C has a capacity of 3 litres.

Currently, container A is full to the brim with water, whereas B and C are empty.

You are allowed to transfer water from any one container to the other, but are not allowed to use external water sources such as taps (so no pouring water down the drain and re-filling). You have no access to measuring equipment, and you are not allowed to 'guesstimate' water levels by eye (so, for instance, you cannot pour water from A to B and then do a visual check that they are approximately the same level, or 'half full').

What steps do you need to take to get to a state where 4 litres of water are in A, 4 litres of water are in B, and C is empty?

## 5 Comments:

max: 8_5_3

start: 8_0_0

5_0_3

5_3_0

2_3_3

2_5_1

7_0_1

7_1_0

4_1_3

4_4_0

??

- robert -

That does it.

But I think there's a solution with fewer steps... part 2 is to find that!

It was early in the morning and I didn't have my coffee ... so let me try again:

3_5_0

3_2_3

6_2_0

6_0_2

1_5_2

1_4_3

4_4_0

;oP

Yep, that's the one I had.

This is an old puzzle, but this variant is from Ian Stewart's 'The Magical Maze', a book of 'popular mathematics'. This one is given as an exercise in a chapter which deals with using graphs as a problem-solving technique. (A 'graph' in this context being a diagram of circles - or nodes - and lines - or edges -, which can be used to sketch out a problem as a type of 'tree' - draw out all the possibilities and eventually you'll find the answer).

Here's a page on using a graph to solve the pouring puzzle.

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