# A mathematical game: moving tiles

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?