You are given two jugs, a 4-gallon one and a 3-gallon one. Neither has any measuring marker on it. There is a tap that can be used to fill the jugs with water. How can you get exactly 2 gallons of water into the 4-gallon jug?
Use Breadth -First search i.e. finish expanding each row before going to the next one. It means expanding the {4,0} followed by the {0,3} states before going to their successors on the next row.