## Four Gallons From Two Buckets

You have two buckets. One holds exactly five gallons and the other three gallons. How can you measure exactly four gallons of water into the five gallon bucket?

Assume you have an unlimited supply of water and that there are no measurement markings of any kind on the buckets.

1. Fill the 3-gallon bucket.
2. Pour the 3 gallons of water into the 5-gallon bucket
3. Fill the 3-gallon bucket again.
4. Fill up the 5-gallon bucket with the 3-gallon bucket, leaving you with 1 gallon left in the 3-gallon bucket.
5. Empty out the 5-gallon bucket.
6. Pour the remaining 1 gallon of water from the 3-gallon bucket into the 5-gallon bucket.
7. Fill the 3-gallon bucket.
8. Pour the 3 gallons of water from the 3-gallon bucket into the 5-gallon bucket leaving you with 4 gallons of water in the 5-gallon bucket.

Alternate solution:

1. Fill up the 5 gallon bucket
2. Pour it into 3 gallon bucket, leaving 2 gallons
3. Empty out the 3 gallon bucket
4. Pour the 2 gallons in the 5 gallon bucket into the 3 gallon bucket
5. Fill up the 5 gallon bucket and pour it into the 3 gallon bucket until it’s full, leaving 4 gallons in the 5 gallon bucket.
Posted in Brain Teasers

29 Comments on "Four Gallons From Two Buckets"

Ryan Walton says
December 23, 2014 @ 10:09

Fill up the 5 gallon bucket till it’s topped off. Pour the water in the five gallon bucket into the 3 gallon bucket. Leaving you with 2 gallons in the 5 gallon bucket and a full 3 gallon bucket. Now empty the 3 gallon bucket and pour the 2 gallons in the 5 gallon bucket into the 3 gallon bucket. Now fill up the 5 gallon bucket till it’s topped off and pour the water in the 5 gallon bucket into the 3 gallon bucket until full. This will give you a full 3 gallon bucket and 4 gallons exactly in the 5 gallon bucket.

February 17, 2015 @ 03:34

Fill the 3 gallon bucket. Pour the water from 3 gallon bucket into 5 gallon bucket. Now there is room for two gallons in the 5 gallon bucket. Fill again the 3 gallon bucket. Pour the water from 3 gallon bucket into 5 gallon bucket. This fills the two gallons room in the 5 gallon bucket and leaves one gallon in the 3 gallon bucket. Drain the water in the 5 gallon bucket. Pour the one gallon water from 3 gallons into 5 gallons. Now there is one gallon of water in 5 gallons bucket. Fill the 3 gallon bucket and pour into 5 gallon bucket. Now the water adds up to four gallons in the 5 gallon bucket.

Steven Roth says
March 12, 2015 @ 00:26

WHY IS EVERYONE WRONG?

Fill the five half way.

Fill the three half way.

Then pour 3 into 5 and you have 4 gallons.

2.5 + 1.5 = 4

LEARNED THIS IN ELEMENTARY SCHOOL

How do you tell when it’s exactly half full?

Collin C says
April 3, 2015 @ 04:06

Steven Roth, the problem with your theory is that its not precise!

Alejandro castillo says
April 17, 2015 @ 01:51

of course is precise. unless you are so picky as to say that the error is bigger than 1% finding the half of something is very precise. and if you disagree then due to capillarity the proposed solution will also not be precise.

M.A. says
April 27, 2015 @ 21:38

Since it was not specified any further the details of the buckets, my original thought was that you could:
1) Take the 3 gallon bucket and place it upside down in the 5 gallon bucket.
2) This leaves room for two gallons in the 5 gallon bucket so fill it up.
3) Take the 3 gallon bucket out of the 5 gallon bucket, leaving the two gallons in the 5 gallon.
4) Pour the two gallons into the 3 gallon bucket.
5) Take the 5 gallon bucket and flip it upside down over the 3 gallon bucket.
6) Carefully invert it so that the 5 gallon bucket is right side up again and the 3 gallon bucket is upside down (inside of the five gallon bucket) and has the two gallons of water inside of it still.
7) Fill up the 5 bucket to the top, giving you 2 more gallons.
8) Take out three gallon bucket and you’re left with 4 gallons of water.

@M.A. That’s a very creative approach, I like it.

Tori says
April 28, 2015 @ 22:10

The very definition of precise is how far to the right of the problem you go. The method using “half-buckets” is the very opposite of precise. I would argue, however, that the answer is quite accurate.

Accurate-how close to the right answer it is.

Precise-how carefully you measure it.

May 4, 2015 @ 15:48

Hi,

The “Half bucket” approach does not work because the buckets are assumed to be straight walled.

If they were angled walls, as some buckets are, the half way approach wouldn’t work and the error could be more than just being generally imprecise. It would be totally flawed as the top of the bucket and bottom of the bucket might have totally different diameters.

Thomas says
June 5, 2015 @ 10:40

@Steven Roth, bro… then back to elementary school… because you missed something.

@M.A. Nice, but I would have just moved the 2 into the three, filled the 5’r up again, and poured off the 1 gallon into the 3, leaving 4 in the 5… 1 less move :D, Also removes the need for ‘carefully inverting’.

Cheers
-T

Saud says
July 1, 2015 @ 03:42

It’s simple as question suggest you have unlimited water and need exactly 4 gallons then all you have to do is.

1. Fill the 5 gallons bucket.
2. Pour the water from the 5 gallons bucket into the 3 gallons bucket.
3. Now 2 gallons of water is remaining in the 5 gallons bucket.
4. Empty the 3 gallons bucket and now pour the 2 gallons of water from the 5 gallons bucket in it.
5. Now fill the 5 gallons bucket with water.
6. Pour the water into the 3 gallons bucket it will only take 1 gallon as it already has 2 gallons in it, so the 5 gallons of bucket will now be left with 4 gallons of water.

RAYn says
October 5, 2015 @ 11:54

Turn the empty 5g upside down so it doesn’t collect rain while the 3g fills up.
Pour the full 3g into the empty 5g, then let it rain into both containers until the available 2g space in the 5g fills. You now have 2g in the 3g and a full 5g.
Pour 1g in the 5g out into the 1g of space remaining in the 3g container and you are left with 4g in the 5g container.
Figure out what the heck you needed exactly 4g of water for before the rain fills the 5g to the top.

Ben says
February 13, 2016 @ 09:37

How do you know when the buckets are half full Steven? The only person who is wrong is you ?

Lazy says
February 16, 2016 @ 12:15

So much for the .5 approach.

Since you can measure/approximate the water, Why do you bother filling both up halfway if you can just fill in the 5gal bucket with just 4gal? Duh. It’s just 1 step.

But then, that’s not the goal of the riddle, is it?

John cossack says
April 15, 2016 @ 17:37

Fill the 3 gallon up with water until full

Pour that into the empty 5 gallons jug leaving space for two more gallons.

Fill up the 3 gallon again and fill the remaing 2 gallons left in the 5 gallon.

Now the 3 gallon jug has 1 gallon and the 5 is full.

Dump out the 5 gallon until empty.

Pour the 1 gallon that is in the 3 gallon into the empty 5 gallon leaving the 3 gallon empty and the 5 gallon with the 1 gallon.

Fill up the 3 gallon until full and then pour it into the 5 gallon jug, joining the 3 gallons with the 1 gallon in the 5 gallon jug.

The 5 gallon jug now has exactly 4 gallons in it.

John cossack says
April 16, 2016 @ 14:11

@M.A. That won’t work. It’s not exact. You aren’t acounting for the thickness of the “bucket” to displace slightly more than three gallons of water. And the secondly, why even bother with this displacement method with air when you can just as easily use the water to displace more water.

For instance a 3 gallon bucket in a 5 gallon filled up ~= 2 gallons of water.
But a 5 gallon bucket of water filled up and poured into the 3 gallon bucket leaves the same 2 gallons in the 5 gallon bucket only more precise.

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