$2\mathrm{.}1(8$ points$)$ Describe the problem space consisting of state representation, start state, goal state $($can be implicit$)$ and operators.

$2\mathrm{.}2(3$ points$)$ What is its branching factor?

$2\mathrm{.}3(4$ points$)$ What is the cost associated with a state and an edge? $($hint: start with the cost of the state. The cost of the edge will be calculated based on that!$)$