How to make a universal algorithm for checking a combination of tags for solvability?

Question

C++ / C#

There is a two-dimensional array, all cells of which are filled with random non-repeating numbers, except for one. The position of an empty cell in an array is always different. How to make sure that the generated combination is solvable? I found several examples of describing such an algorithm on the Internet, but they did not help.

Answer 1

Count the number of inversions. If odd, there is no solution.