Water Jug Problem

Given a 5-gallon jug and a 2-gallon jug, with the 5-gallon jug initially full of water and the 2-gallon jug empty, the goal is to fill the 2-gallon jug with exactly one gallon of water.

State = (x,y), where x = number of gallons of water in the 5-gallon jug and y is gallons in the 2-gallon jug
Initial State = (5,0)
Goal State = (*,1), where * means any amount
Operators
- (x,y) -> (0,y) ; empty 5-gal jug
- (x,y) -> (x,0) ; empty 2-gal jug
- (x,2) and x<=3 -> (x+2,0) ; pour 2-gal into 5-gal
- (x,0) and x>=2 -> (x-2,2) ; pour 5-gal into 2-gal
- (1,0) -> (0,1) ; empty 5-gal into 2-gal

State Space (also called the Problem Space)

                     (5,0) = Start
		     /  \
                 (3,2)  (0,0)
                  / \
              (3,0) (0,2)
               /
           (1,2)
            /
        (1,0)
	 /
     (0,1) = Goal

There are few states, and almost no choice of actions, so the problem is very easy to search.