## 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.

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

- Fill up the 5 gallon bucket
- Pour it into 3 gallon bucket, leaving 2 gallons
- Empty out the 3 gallon bucket
- Pour the 2 gallons in the 5 gallon bucket into the 3 gallon bucket
- 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.

Dheeraj Jonnalagadda says

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

Dan says

March 12, 2015 @ 00:31

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.

Dan says

April 28, 2015 @ 10:45

@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.

Neeraj Madan says

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.

John Cena says

May 8, 2016 @ 09:02

Yo, Everyone,

What the hell is wrong with you?

How are any of your answers possible, *REMINDER* there are two buckets, one is able to hold 5 gallons and one is able to hold 3 gallons.

Even though it is possible to fill a 5 gallon bucket with 4 gallons of water, it is impossible to fill a 3 gallon bucket with 4 gallons, because all the water will fall out.

Your welcome for my smartness

JOHN CENA

Mike B. says

May 10, 2016 @ 00:13

I love the creativity of these solutions, however:

1) The “halfway technique”: Funny, I first heard this problem on Die Hard 3, and then later in remedial algebra my freshman year of high school. I solved it one of the correct ways then (method 1 of “the answer”) without the inherent imprecision of Steven Roth’s method. I guess the implications of bombs blowing up really helps to solidify the seriousness of precision versus accuracy.

2) As John Cossack pointed out, the “inversion technique” fails to account for the wall thickness (a dimension not given in the problem statement though unlikely to be zero).

3) The “rain technique” fails to account for the random distribution of rain drops, though the statistical significance of this phenomenon remain dubious. See:

https://www.quora.com/Does-Rain-fall-evenly-If-I-could-measure-the-locations-on-which-rain-drops-fall-DIRECTLY-no-splashes-on-the-sidewalk-would-I-get-an-even-spread-Or-will-I-see-dry-spots

It’s probably more precise than the “pouring technique” given you could not spill a drop and you would have to empty the containers completely every time.

All in all, I don’t know of any way with dead-on precision except through measurement on a scale and knowing the density of water at a given temperature and pressure See:

https://www.ncsu.edu/chemistry/resource/H2Odensity_vp.html or http://www.engineeringtoolbox.com/water-density-specific-weight-d_595.html if you really want to geek out

The only way for this method to be truly effective is to have instruments with more precision than the method used to confirm the four gallons of water.

(And don’t get me started on taking true temperature readings or the purity of the water in question!)

Grace says

May 16, 2016 @ 11:27

Everyone here so far is wrong. You fill the 3 gallon bucket up, and then pour it into the 5 gallon bucket. You then fill the 3 gallon bucket up again and pour it into the 5 gallon bucket until the 5 gallon bucket is filled, which leaves you with 1 gallon of water in the 3 gallon bucket. You then pour out the 5 gallon bucket, fill it up with the 1 gallon in the 3 gallon bucket, then fill the 3 gallon bucket up again and pour it into the 5 gallon bucket. There is now 4 gallons in the 5 gallon bucket.

Jonny says

August 12, 2016 @ 15:16

Fill 5 gallon bucket.

Poor into 3 gallon bucket.

Poor the remaining 2 gallons from the 5 gallon bucket into the 4 gallon bucket.

Repeat.

Jonny says

August 12, 2016 @ 15:21

Disregard. I didn’t read the whole thing. They had a similar puzzle in Star Wars KOTR that had also had a 4 gallon bucket.

Roody says

August 23, 2016 @ 22:19

Fill up the 3 gallon and pour it in the 5 gallon. Then fill up the 3 gallon AGAIN and pour in the 5 gallon until there is 1 gallon left in the 3 gallon. Then, dump out the 5 gallon completely. Then fill the 5 gallon with the one gallon leftover in the 3 gallon. Then fill up the 3 gallon one last time and pour it in the 5 gallon

Andribbles says

September 20, 2016 @ 16:55

1) fill up the five gallon bucket

2) pour it into the three gallon bucket

You have 2 gallons in the 5 gallon bucket and 3 gallons in the 3 gallon bucket

3) dump out the five gallon bucket

4) pour the 3 gallon into the 5 gallon

You have 3 gallons in the 5 gallon bucket and 0 gallons in the 3 gallon bucket

5) Fill the 3 gallon bucket and pour it into the 5 gallon bucket.

6) pour out the 3 gallon bucket

You now have 4 gallons in the 5 gallon bucket and 0 gallons in the 3 gallon bucket

Done.

Robin Clark says

January 22, 2017 @ 12:38

Done in 3 Steps.

Step 1: Fill 5 G, pour into 3 G (Leaving 2 G in 5)

Step 2: Pour Remaining 2 G into 3 G,

Step 3: Fill 5 G, Pour off 1 G, filling 3 G, Voila Exactly 4 G Remaining.

note: on exactness, answer in question context ( Remember your using unmarked buckets)

Eric says

April 11, 2017 @ 23:34

4 gallons? You already have 8 gallons between both buckets, you all are wasting water lol

virtual.Don says

June 27, 2017 @ 00:38

1. Sell the 3 gallon bucket and use the proceeds to by tape measure. Mark off the 5 gallon bucket and fill it till it’s 4/5 full!

2. Sell the 3 gallon bucket and buy a scale. Place the 5 gallon bucket on the scale and note the weight. Fill with water until it is 33 lbs, 6oz heavier.

Ishtiaq says

July 19, 2017 @ 04:45

First take 5 gallon full bucket, pour 3 gallon in other 3 gallon bucket.

5-3=2 gallons remaining in 5 gallon bucket

Empty now the 3 gallon bucket.

Put these 2 gallons (from 5 gallon bucket) into 3 gallons bucket.

Now again make full the 5 gallons bucket.

Put 1 gallon into 3 gallon bucket ( having already 2 gallons means total now 2+1=3)

and The 5 gallon bucket now have 4 Gallon water… USE 4 gallon water now.. and enjoy…

brittany says

September 16, 2020 @ 13:49

got it right in the first place

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