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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.
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28 Comments on "Four Gallons From Two Buckets"


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…


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