# Trying to find a water measuring puzzle

I am trying to find this puzzle which I once came across as a kid, but can't seem to recall it properly now (or find it). It goes something like this.

There is a reservoir of capacity 20 litres filled with water. You have 2 buckets of volume x and y (can't seem to recall this information). Without any other forms of measurement, the final aim is to have 2 litres in both buckets. Does anyone remember this puzzle ? It might have been by Lewis Carroll. The values of x,y might have been 3,4 or 4,5 but I am 99% positive about the 20 litres and 2 litres part. Would be very helpful if someone can help me find it.

Edit: Thanks for the replies guys, sorry I don't recollect the original puzzle, but from what I remember there was no wasting of water and the supply of water also wasn't infinite.

• It's not possible to have 2 litres left in both buckets. After every "move", one of the buckets is either completely full or completely empty. – Deusovi Sep 26 '15 at 19:43
• @Deusovi, but can you pour into the reservoir? – Going hamateur Sep 26 '15 at 19:44
• @Goinghamateur: If you do that then the bucket you pour in is going to be empty. – Deusovi Sep 26 '15 at 19:45
• @deusovi well what if you get like 7 liters left in the reservoir, then with just the water in the buckets get 2 liters in the 4 liter. Then empty the 5. Then put the reservoir's 2 in the 5. – Going hamateur Sep 26 '15 at 19:46
• There is a post on meta about this question. – Julian Rosen Sep 27 '15 at 15:39

The puzzle as you describe it is impossible.

If no water is wasted and the buckets' capacities are less than 20L, then after every move either one of the buckets is empty or one of the buckets is full. Therefore, there cannot be 2L in both buckets.

• The question is asking for help finding the puzzle. It is not asking for a solution. – dennisdeems Oct 10 '15 at 20:24
• Unless one of the jar is exactly 2L :-) – Mikaël Mayer Oct 15 '15 at 20:34

The puzzle you seek is a variant of a classic that exists in several versions. There does not seem to be a single definitive source.

A version of the puzzle was presented in the movie Die Hard: With a Vengeance, which, I'm guessing, is where most people today have encountered it: "provided with an unlimited water supply, a 5-gallon jug, and a 3-gallon jug, measure out precisely 4 gallons, by filling and emptying the jugs."

It has been attributed to Siméon Denis Poisson, but apparently there are much older versions, for example one by Luca Pacioli from the 15th century.

Here is a source that discusses the puzzle and touches on its history and some of its different versions: http://www.pballew.net/PatBlogs.html/221

• Care to explain, downvoter? – dennisdeems Oct 13 '15 at 18:32

Assuming the buckets have equal surface on bottom and top there is a very easy solution

Fill the 4l bucket, pour water into the 5l one till you see the back corner of the bucket; done

Other then this there is no solution where you fill both buckets, not without wasting water or using a second reservoir.

• The question is asking for help finding the puzzle. It is not asking for a solution. – dennisdeems Oct 10 '15 at 20:24
• @dennisdeems It is asking for help finding the puzzle, however the OP seems to have a pretty clear idea in his mind of what the puzzle was. Definetely 2l, No spillage, 2 Buckets.. Now what he proposes is impossible, pouring from 1 to another always leaves 1 empty or 1 full, unless there's spillage (or a trick) involved. This is probably the reason OP believes his recollection to be faulty. Presenting him with a solution might make him reconcile his memories into the 'correct' puzzle. (The solution I present has been shown on a TV program when i was younger, and might be the source.) – DrunkWolf Oct 12 '15 at 11:59
• Fair enough, but probably more appropriate as a comment then? – dennisdeems Oct 12 '15 at 14:37
• @dennisdeems Perhaps, in hindsight that would've been best probably. Such an unusual question though, but you're ultimately right. – DrunkWolf Oct 12 '15 at 14:52

For 2 litres in each bucket first take Saurabh Prajapati's solution(Trying to find a water measuring puzzle) until the end.

We now have

$Y(5l)=5, X(4l)=2, R=13.$

Empty Y into R and fill the 2 litres of X into Y afterwards:

$Y=2, X=0, R=18$

Now we fill X completely and empty it into the ground. Do that 4 times:

$Y=2, X=0, R=2$

Now we only need to fill the 2 litres from R into X:

$Y=2, X=2, R=0$

• " Now we fill Y completely and empty it into the ground. Do that 4 times: " You mean X here? – Kevan St. John Oct 9 '15 at 18:21
• doesn't pouring 16 litres of water on the ground count as wasting water? If you posit some other container to put the 16 litres in, you have the same extra rules as I do, namely a spare container that is not used for measuring but is nonetheless used. – Kate Gregory Oct 10 '15 at 16:50
• The question is asking for help finding the puzzle. It is not asking for a solution. – dennisdeems Oct 10 '15 at 20:24

If "Without any other forms of measurement" still allows me to have a random bucket of unknown capacity, and I can pour water back into the reservoir, then it can be done. If the difference between the two buckets is 2L, it's trivial. Fill the larger one, then carefully pour from the larger into the smaller. The larger now contains the difference (2L). Pour this into the extra bucket.

Do it again and you have 2L in the larger bucket. Pour the smaller one back into the reservoir and fill it from the extra bucket. Done!

If the difference is 1L, you need more extra buckets.