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Games!, Stuff about Math

Solution to the Water Jug Problem.

If you don’t know what the Water Jug Problem is, click on the link first before you go on. For those who’ve read it, and consequently tried to answer it, I’ll refresh you on the problem.

We have three water jugs, and each can hold 8oz., 5oz., and 3oz. of water, respectively. Without the possibility of water spilling when poured from one jug to another, and given that the jugs have no calibration, how do we divide the 8oz. of water equally among two jugs?

To illustrate, from:





What I’m going to do is to draw these jugs into:

I said that the jugs aren’t calibrated, and they’re not calibrated here either. It’s easier to understand when we can see what’s going on. We have to remember though, that when we pour from one jug to another, it must either fill the jug where water is being poured into, or until the other jug becomes empty.

I will show the solution I have here. These are all trial-and-error stuff, so I guess with a little persistence, you’ll be able to get the solution. Read the captions so you know what I did in that step.


1. We pour water from 8oz. jug to 5oz. jug, leaving 3oz. in the 8oz. jug.


2. We pour water from the 5oz. jug to the 3oz. jug, leaving 2oz. in the 5oz. jug.

3. We pour water from the 3oz. jug to the 8oz. jug. The 8oz. jug now has 6oz. of water in it.

4. We pour all the water from the 5oz. jug to the 3oz. jug.

5. We pour water from the 8oz. jug to the 5oz. jug, leaving 1oz. in the 8oz. jug.

6. We pour 1oz. of water from the 5oz. jug to the 3oz. jug to fill it. The 5oz. of jug now has 4oz. of water. We are close!

7. Last step! We pour water from the... oh, do I have to explain this one? No? Then we're done.

.     .     .

There you go. Fun, right? What did I tell you?

I want to share this website with you. It’s got a simple program where you can try out the solution for the three jugs problem, as well as taking a look at how the Barycentric Coordinate System can be used to solve it.



About ceteris2008

Math Major. Musician.


4 thoughts on “Solution to the Water Jug Problem.

  1. wow… its gonna be gud and nice exercise..

    Posted by punit | May 10, 2011, 11:01 pm
  2. Really it is very useful for me……..thanks

    Posted by Anonymous | August 6, 2011, 5:12 pm
  3. Thanks so much!!!!

    Posted by Anonymous | May 23, 2012, 9:01 am
  4. thanks bro..

    Posted by Yohanes Rizky | February 20, 2015, 1:13 am

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