There is a mathematical game called moving tiles.
There are $8$ different movable tiles on a $3 \times 3$ board,
At the beginning the tiles' location is given as following:
-------------------
| 1 | 2 | 3 |
-------------------
| 5 | 6 | 7 |
-------------------
| 8 | 9 | |
-------------------
Each time you can only move one tile to the blank, which is next to the blank.
As an example, the fist move must be one of the following situations:
-------------------
| 1 | 2 | 3 |
-------------------
| 5 | 6 | |
-------------------
| 8 | 9 | 7 |
-------------------
or
-------------------
| 1 | 2 | 3 |
-------------------
| 5 | 6 | 7 |
-------------------
| 8 | | 9 |
-------------------
I want to prove that the following situation is impossible according to the rules:
-------------------
| 1 | 2 | 3 |
-------------------
| 5 | 6 | 7 |
-------------------
| 9 | 8 | 0 |
-------------------
Maybe I should use graph theory or group theory, can anyone help?
