diff --git a/DIRECTORY.md b/DIRECTORY.md
index d3a378c3a2ee..80859356cca9 100644
--- a/DIRECTORY.md
+++ b/DIRECTORY.md
@@ -473,6 +473,7 @@
   * [Binary Exponentiation 2](https://github.com/TheAlgorithms/Python/blob/master/other/binary_exponentiation_2.py)
   * [Detecting English Programmatically](https://github.com/TheAlgorithms/Python/blob/master/other/detecting_english_programmatically.py)
   * [Dijkstra Bankers Algorithm](https://github.com/TheAlgorithms/Python/blob/master/other/dijkstra_bankers_algorithm.py)
+  * [Doomsday](https://github.com/TheAlgorithms/Python/blob/master/other/doomsday.py)
   * [Euclidean Gcd](https://github.com/TheAlgorithms/Python/blob/master/other/euclidean_gcd.py)
   * [Fischer Yates Shuffle](https://github.com/TheAlgorithms/Python/blob/master/other/fischer_yates_shuffle.py)
   * [Frequency Finder](https://github.com/TheAlgorithms/Python/blob/master/other/frequency_finder.py)
@@ -487,6 +488,7 @@
   * [Lru Cache](https://github.com/TheAlgorithms/Python/blob/master/other/lru_cache.py)
   * [Magicdiamondpattern](https://github.com/TheAlgorithms/Python/blob/master/other/magicdiamondpattern.py)
   * [Markov Chain](https://github.com/TheAlgorithms/Python/blob/master/other/markov_chain.py)
+  * [Max Sum Sliding Window](https://github.com/TheAlgorithms/Python/blob/master/other/max_sum_sliding_window.py)
   * [Nested Brackets](https://github.com/TheAlgorithms/Python/blob/master/other/nested_brackets.py)
   * [Palindrome](https://github.com/TheAlgorithms/Python/blob/master/other/palindrome.py)
   * [Password Generator](https://github.com/TheAlgorithms/Python/blob/master/other/password_generator.py)
@@ -529,7 +531,6 @@
     * [Sol2](https://github.com/TheAlgorithms/Python/blob/master/project_euler/problem_06/sol2.py)
     * [Sol3](https://github.com/TheAlgorithms/Python/blob/master/project_euler/problem_06/sol3.py)
     * [Sol4](https://github.com/TheAlgorithms/Python/blob/master/project_euler/problem_06/sol4.py)
-    * [Test Solutions](https://github.com/TheAlgorithms/Python/blob/master/project_euler/problem_06/test_solutions.py)
   * Problem 07
     * [Sol1](https://github.com/TheAlgorithms/Python/blob/master/project_euler/problem_07/sol1.py)
     * [Sol2](https://github.com/TheAlgorithms/Python/blob/master/project_euler/problem_07/sol2.py)
@@ -595,11 +596,11 @@
   * Problem 26
     * [Sol1](https://github.com/TheAlgorithms/Python/blob/master/project_euler/problem_26/sol1.py)
   * Problem 27
-    * [Problem 27 Sol1](https://github.com/TheAlgorithms/Python/blob/master/project_euler/problem_27/problem_27_sol1.py)
+    * [Sol1](https://github.com/TheAlgorithms/Python/blob/master/project_euler/problem_27/sol1.py)
   * Problem 28
     * [Sol1](https://github.com/TheAlgorithms/Python/blob/master/project_euler/problem_28/sol1.py)
   * Problem 29
-    * [Solution](https://github.com/TheAlgorithms/Python/blob/master/project_euler/problem_29/solution.py)
+    * [Sol1](https://github.com/TheAlgorithms/Python/blob/master/project_euler/problem_29/sol1.py)
   * Problem 30
     * [Sol1](https://github.com/TheAlgorithms/Python/blob/master/project_euler/problem_30/sol1.py)
   * Problem 31
@@ -656,6 +657,8 @@
     * [Sol1](https://github.com/TheAlgorithms/Python/blob/master/project_euler/problem_63/sol1.py)
   * Problem 67
     * [Sol1](https://github.com/TheAlgorithms/Python/blob/master/project_euler/problem_67/sol1.py)
+  * Problem 71
+    * [Sol1](https://github.com/TheAlgorithms/Python/blob/master/project_euler/problem_71/sol1.py)
   * Problem 76
     * [Sol1](https://github.com/TheAlgorithms/Python/blob/master/project_euler/problem_76/sol1.py)
   * Problem 97
diff --git a/backtracking/sudoku.py b/backtracking/sudoku.py
index b3d38b4cc7c7..614bdb8530ac 100644
--- a/backtracking/sudoku.py
+++ b/backtracking/sudoku.py
@@ -1,3 +1,7 @@
+from typing import List, Tuple, Union
+
+Matrix = List[List[int]]
+
 """
     Given a partially filled 9×9 2D array, the objective is to fill a 9×9
     square grid with digits numbered 1 to 9, so that every row, column, and
@@ -36,7 +40,7 @@
 ]
 
 
-def is_safe(grid, row, column, n):
+def is_safe(grid: Matrix, row: int, column: int, n: int) -> bool:
     """
     This function checks the grid to see if each row,
     column, and the 3x3 subgrids contain the digit 'n'.
@@ -55,7 +59,7 @@ def is_safe(grid, row, column, n):
     return True
 
 
-def is_completed(grid):
+def is_completed(grid: Matrix) -> bool:
     """
     This function checks if the puzzle is completed or not.
     it is completed when all the cells are assigned with a non-zero number.
@@ -76,7 +80,7 @@ def is_completed(grid):
     return all(all(cell != 0 for cell in row) for row in grid)
 
 
-def find_empty_location(grid):
+def find_empty_location(grid: Matrix) -> Tuple[int, int]:
     """
     This function finds an empty location so that we can assign a number
     for that particular row and column.
@@ -87,7 +91,7 @@ def find_empty_location(grid):
                 return i, j
 
 
-def sudoku(grid):
+def sudoku(grid: Matrix) -> Union[Matrix, bool]:
     """
     Takes a partially filled-in grid and attempts to assign values to
     all unassigned locations in such a way to meet the requirements
@@ -124,7 +128,7 @@ def sudoku(grid):
     return False
 
 
-def print_solution(grid):
+def print_solution(grid: Matrix) -> None:
     """
     A function to print the solution in the form
     of a 9x9 grid