Many of you might have heard about the famous problem of water and jugs. It goes as follows:

There are **n** jugs each having particular capacity (all unique) and unlimited supply of water. The problem is to find whether a particular value, say **w,** be measured from the given jugs.

To make it simple, say there are **2** jugs of capacity **5L** and **3L** each. The problem is to find whether **4L ** can be measured?

Well many of you know the solution, and it can be found at many of the places!!!

* Fill the 3l, pour into 5l

* Fill the 3l, pour into 5l (1l remaining in 3l jug)

* Empty the 5l an pour into it the water from 3l, that is 1l

* Fill the empty 3l and pour into 5l jug and done.

**What to do with diophantine equations?**

I am not sure!!! but this one could be possible.

Let the capacities be **a,b,c,d** and the final quantity to be measured be **p**, consider the following equation.

**ax + by + cz + dw = p…………………….(1)**

The result which I am not sure of (:D) :

The problem (of water – jug ) has a solution if (1) has solution. (1) has a solution only when gcd (s,b,c,d) = kp, where k = 1,2,3,4,..

How do I verify both problems are the same ??

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