Question 3
Consider the 3-2-1 Water Jug puzzle with three jugs A, B and C of capacities 3L, 2L and 1L, respectively.
A state is uniquely represented by the amount of water present in the three jugs, for example, the tuple (3,0,0) describes the state where jug A contains 3L of water and jugs B and C are empty. Two basic (atomic) moves are allowed: (1.) pick up a jug and fill up (top up) another jug, and (2.) pick up a jug and empty it into another jug, without spilling any water in the process. Start from (3,0,0) and construct the state space graph of this puzzle.
Which of the following states occur in the state space graph?