Q: Can we construct a complete graph of the 8-puzzle problem space as
we can for the
FWGC
problem or the water jug problem?
Such a graph would have to include every possible state of the 8-puzzle.
Q: About how many states is that?
The number of possible arrangements of tiles is 9! = 362,880.
The number of states is smaller (not every random arrangement of tiles can reach
the final state) but still too large to enumerate by hand.