1. Consider a state space where the start state is number 1 and each state k has two successors: numbers 2k and 2k + Suppose the goal state is 2019. Can you find an algorithm that outputs the solution to this problem without any search at all? (6 points)
2. 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. We can formulate this problem as follows. Well define the coordinate system so that the center of the maze is at (0, 0), and the maze itself is a square from (1, 1) to (1, 1).

3. Initial state: Robot at coordinate (0, 0), facing North.

   Successor function: Move forwards any distance d; change direction robot is facing. Cost function: Total distance moved.

4. 1. Let (x, y) be the current location. What is the Goal test? (2 points)
   2. How large is the state space? (2 points)