While reading through some lecture notes on preliminary number theory, I came across the solution to
water jug problem (with two jugs) which is summed as thus:
Using the property of the G.C.D of two numbers that GCD(a,b) is the smallest possible linear combination of a and b, and hence a certain quantity Q is only measurable by the 2 jugs, iff Q is a n*GCD(a,b), since Q=sA + tB, where:
n = a positive integer A = capacity of jug A B= capacity of jug B
And, then the method to the solution is discussed
Another model of the solution is to model the various states as a state-space search problem as often resorted to in Artificial Intelligence.
My question is: What other known methods exist which models the solution, and how? Google didn't throw up much.