Why is this 8-puzzle solvable?

Question

So i am writing a program to solve 8 puzzle using BFS,A*, and UCS. The goal state is fixed according to the assignment which is given as:

Goal State:
|1 2 3|
|8   4|
|7 6 5|   

My Initial State:
|  1 2| 
|8 4 3| 
|7 6 5|

However, upon writing a getInvCount(int [] a) method:

public static boolean getInvCount(int [] a)
{
    int [] arr = a;
    int inv_count = 0;
    for(int i = 0;i<arr.length-1;i++){
        for(int j = i + 1; j < arr.length;j++){
            if(arr[i]>arr[j]){
                inv_count++;
                
            }
        }
        
    }
    System.out.println(inv_count);

I realize that the initial puzzle has 9 inversions which is an odd number. Yet the program successfully finds the solution. Is there something I am missing in the requirements for a puzzle to be deemed solvable?

Answer 1

Your getInvCount function is only valid for the "1 2 3 4 5 6 7 8" goal state. An "inversion" is when two tiles are in a different order than they are in the goal state. The comparison arr[i] > arr[j] is only a correct check for an inversion if the goal state is strictly increasing.