This problem is defined as the map-coloring problem. Goal: assign a color to each territory on the map. Constraints: adjacent territories must not share the same color. For example, if Western Australia is colored blue, then Northern Territory must be red or green. Domain: Colors that may be used are Red, Green, and Blue. How many solutions are there for the map-coloring problem in Australia as shown in the attached figure if three colors are allowed to use? Please justify your answer.

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