Friday, October 15, 2004

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:

Anonymous Anonymous said...

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 -

October 16, 2004 at 2:26 AM  
Blogger steven said...

That does it.

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

October 16, 2004 at 11:55 AM  
Anonymous Anonymous said...

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

October 16, 2004 at 1:44 PM  
Blogger steven said...

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).

October 18, 2004 at 1:33 PM  
Blogger steven said...

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

October 18, 2004 at 1:37 PM  

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