fix: Ensure Number Sliding Puzzle is solvable (steam-bell-92#1158)

- Implement is_solvable helper function using inversion counts
- Update shuffle loop to generate only solvable puzzles
- Avoid generating an already-solved board on start
- Add unit tests to verify is_solvable logic on various configurations

Author: nishtha-agarwal-211

games/Number-Sliding-Puzzle/Number-Sliding-Puzzle.py

@@ -8,14 +8,37 @@
 from utils.validation import get_int, get_yes_no
 
 
+def is_solvable(numbers):
+    """
+    Determines if the 8-puzzle board configuration is solvable.
+    An 8-puzzle (3x3 grid) is solvable if the number of inversions is even.
+    The blank tile (0) is ignored when counting inversions. 
+    """
+    # Filter out the blank tile(0)
+
+    tiles = [n for n in numbers if n != 0]
+    inversions = 0
+    for i in range(len(tiles)):
+        for j in range(i + 1, len(tiles)):
+            if tiles[i] > tiles[j]:
+                inversions += 1
+
+    # return True if inversions count is even, False otherwise
+
+    return inversions % 2 == 0
+
+
 def main():
     print("🧩 Emoji Sliding Puzzle Game 🧩")
 
     while True:
         print("Arrange the numbers in correct order!\n")
 
         numbers = [1, 2, 3, 4, 5, 6, 7, 8, 0]
-        random.shuffle(numbers)
+        while True:
+            random.shuffle(numbers)
+            if is_solvable(numbers) and numbers != [1, 2, 3, 4, 5, 6, 7, 8, 0]:
+                break
 
         puzzle = [
             numbers[0:3],