Q$1.(10$ Points$)$

a$)$ Provide a standard problem formulation for the following as a search problem$($states$,$ initial state, goal state, actions, transition model, action cost function$)$: Given the initial state where both a $21-$gallon jug and a $26-$gallon jug are empty, our objective is obtaining exactly $3$ gallons of water. There are no restrictions on the number of pours or emptying operations, and there is an abundant water supply available. Assume each action of emptying a jug or pouring water from one jug to another costs $1.$ Also, assume the state of the system at each step is described with a pair of numbers $(x,y),$ where $x$ is the amount of water in the jug with capacity $21$ and $y$ is the amount in the jug with capacity $26.(4$ points$)$

b$)$ What is the size of the state space when measured in terms of possible operations? $(2$ points$)$

c$)$ Determine the optimal sequence of actions $($minimal action cost$)$ to achieve the goal of obtaining exactly $3$ gallons of water. $(4$ points$)$

Answer: