How many solutions are there for the map$-$coloring problem in Figure $6\mathrm{.}1$ in the text? How many solutions if four colors are allowed? Two colors?Figure $6\mathrm{.}1($a$)$ The principal states and territories of Australia. Coloring this map can be viewed as a constraint satisfaction problem $($CSP$).$ The goal is to assign colors to each region so that no neighboring regions have the same color. $($b$)$ The map$-$coloring problem represented as a constraint graph.