Problem $2$

In the three jars problem, a situation arises in which there are three jars or containers of capacities A$,$ B and C liters $($integers$)$ with A $>$ B $>$ C and A even. Initially, the largest jar is full and the other two are empty. The objective is to distribute the initial content equally between the two largest jugs, correctly transferring the water between the jugs. For example, for the problem A $=8,$ B $=5,$ and C $=3,$ there are initially $8$ liters in jar A$,$ and the rest of the jars are empty. Then, in the end, jars A and B would be left with $4$ liters and jar C would be empty.For this problem:

$1.$ Pose the puzzle for A $=8,$ B $=5,$ and C $=3$ as a search problem, in which you want to determine the sequence of transfers to achieve the objective of having the two largest capacity jars with the same amount of water.

$2.$

To do this, formally describe the problem.If you want to use a heuristic search algorithm, what heuristic function do you think could work? Because?

$3.$Develop the first $4$ levels of the search tree with the heuristic algorithm of your choice. Clearly indicate the heuristic function used