Question 1 (8 points): Give a complete problem formulation for each of the following. Choose a formulation that is precise enough to be implemented. (a) Using only four colors, you have to color a planar map so that no two adjacent regions have the same color. (4 points) (b) You have three jugs, measuring 12 gallons, 8 gallons, and 3 gallons, and a water faucet. You can fill the jugs up or empty them out from one to another or onto the ground. You need to measure out exactly one gallon. (4 points) Question 2 (17 points): Consider a state space where the start state is number 1 , and each state k has two successors: numbers 2k and 2k+1. (a) Draw the portion of the state space for states 1 to 15. (2 points) (b) Suppose the goal state is 11 . List the order in which nodes will be visited for breadth-first search and depth-limited search with limit 3 . (8 points) (c) How well would bidirectional search work on this problem? What is the branching factor in each direction of the bidirectional search? (4 points) (d) Does the answer to (c) suggest a reformulation of the problem that would allow you to solve the problem of getting from state 1 to a given goal state with almost no search? (3 points)