8-puzzle problem: The puzzle consists of an area divided into a grid, 3 by 3. On each grid square is a tile, except for one square which remains empty. A tile that is next to the empty grid square can be moved into the empty space, leaving its previous position empty in turn.
Given any initial state of the puzzle, there are exactly $ 9!/2$ reachable states. How do I prove this? And how should I generalized the proof to $ (n^2-1)$ -puzzle problem derived using $ n$ by $ n$ grid?