JAVA know if a Puzzle n X n has a solution

I would like to know how to make a code that lets me know if a puzzle n xn (in which I generate random positions [and leave a picture of the game]) has a solution, so I saw not all the different possibilities of generating A puzzle has a solution, I found a code that supposedly told me if it was solvable or not, but I compared results with an online verifier and it's not 100% effective.

//Code
 public boolean isSolvable(List<Integer> puzzle, int squartRoot) {
        int parity = 0;
        int gridWidth = squartRoot;
        int row = 0;
        int blankRow = 0;

        for (int i = 0; i < puzzle.size(); i++) {
            if (i % gridWidth == 0) {
                row++;
            }
            if (puzzle.get(i) == 0) {
                blankRow = row;
                continue;
            }
            for (int j = i + 1; j < puzzle.size(); j++)
            {
                if (puzzle.get(i) > puzzle.get(j) && puzzle.get(j) != 0)
                {
                    parity++;
                }
            }
        }

        if (gridWidth % 2 == 0) {
            if (blankRow % 2 == 0) {
                return parity % 2 == 0;
            } else {
                return parity % 2 != 0;
            }
        } else {
            return parity % 2 == 0;
        }
    }

// Photo of the game

The idea is that it can serve as much 3 x3 as 4 x4 etc u_u "did not manage to make it work correctly