I understand the material in the chapter. However, the exercises are
completely confusing to me. Therefore, a discussion of the chapter may
clarify. For the 8-puzzle problem, I am not able to understand the
existence of two disjoint sets of all possible states in which a state
from one set can't transform to a state in the other set by any number
of moves. I would assume any state can be reached by in other state. In
other words, there are situations (initial state - goal configuration)
in which the puzzle isn't solvable? Does the two disjoint sets exit
because the problem becomes an NP-Complete problem for those states
trying to reach the states in the other disjoint set. And, the 9!/2
calculation for all possible states derives from this theorem of
exactly half of the possible states transform into a given goal, is
this true?