8 puzzle that can be solved or not?

Question

Some of 8 puzzles can be solved if it is transferred from the #12345678. But there are 9! states. How to rule out many of the wrong states use rules that 8 puzzles have potential, like odd and even, the right rule is #12345678, every line only three place and so on.

Answer 1

I can delete some states with the potential rule in parity order.