Can all the 8-puzzle be solved?

   Do you ever play the game below?

   At first, the order of these numbers is in a mess, you can move the number to the blank. If you can place the order you win the game. So if you are given a 8-puzzle can you solve it? At first thought it seems can be solved easily. But it's not true!!!

   Here is the proof:

   Give the note [2 3 1 4 5 6 7 8 9] for the following 8-puzzle:

   Define the inverse order of the sequence. The inverse order of [2 3 1 4 5 6 7 8 9]  is two, for [2,1]，[3,1] is disorder in the sequence.

      The movement when you solve the puzzle never change the even or odd of the inverse order.

      The inverse order of the target order [1 2 3 4 5 6 7 8] is even, Which means if you are given a puzzle, which disorder is odd, you can never solve it.

      You can play the trick on your friend, you already have the magic of math. Math can be the interesting part of life, right?