9. Give a complete problem formulation for each of the following (initial state, goal test,
successor function, cost function). Choose a formulation that is precise enough to be
implemented.
(a) Using only four colors, you have to color a planar map in such a way that no two
adjacent regions have the same color.
(b) A 3-foot-tall monkey is in a room where some bananas are suspended from the 8-foot
ceiling. He would like to get the bananas. The room contains two stackable, movable,
climbable 3-foot-high crates.
(c) You have a program that outputs the message “illegal input record” when fed a certain
file of input records. You know that processing of each record is independent of the other
records. You want to discover what record is illegal.
(d) 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.