Your goal is to navigate a robot out of a maze. The robot starts in the center of the maze facing north. You can turn the robot to face north, east, south, or west. You can direct the robot to move forward a certain distance, although it will stop before hitting a wall.

(a) Formulate this problem. How large is the state space?

(b) In navigating a maze, the only place we need to turn is at the intersection of two or more corridors. Reformulate this problem using this observation.

How large is the states pace now?