4.2 Come up with heuristics for the following problems. Explain whether they are admissible, and whether the state spaces contain local maxima with your heuristic:

a. The general case of the chain problem (i.e., with an arbitrary goal state) from Exercise 3.15.

b. Algebraic equation solving (e.g., "solve jr>'3 = 3 — xy for*").

c. Path planning in the plane with rectangular obstacles (see also Exercise 4.13).

d. Maze problems, as defined in Chapter 3.