Rename Project Euler directories and other dependent changes (#3300)

* Rename all Project Euler directories:

Reason:
The change was done to maintain consistency throughout the directory
and to keep all directories in sorted order.

Due to the above change, some config files had to be modified:
'problem_22` -> `problem_022`

* Update scripts to pad zeroes in PE directories

project_euler/problem_015/sol1.py

@@ -0,0 +1,44 @@
+"""
+Problem 15: https://projecteuler.net/problem=15
+
+Starting in the top left corner of a 2×2 grid, and only being able to move to
+the right and down, there are exactly 6 routes to the bottom right corner.
+How many such routes are there through a 20×20 grid?
+"""
+from math import factorial
+
+
+def solution(n: int = 20) -> int:
+    """
+    Returns the number of paths possible in a n x n grid starting at top left
+    corner going to bottom right corner and being able to move right and down
+    only.
+    >>> solution(25)
+    126410606437752
+    >>> solution(23)
+    8233430727600
+    >>> solution(20)
+    137846528820
+    >>> solution(15)
+    155117520
+    >>> solution(1)
+    2
+    """
+    n = 2 * n  # middle entry of odd rows starting at row 3 is the solution for n = 1,
+    # 2, 3,...
+    k = n / 2
+
+    return int(factorial(n) / (factorial(k) * factorial(n - k)))
+
+
+if __name__ == "__main__":
+    import sys
+
+    if len(sys.argv) == 1:
+        print(solution(20))
+    else:
+        try:
+            n = int(sys.argv[1])
+            print(solution(n))
+        except ValueError:
+            print("Invalid entry - please enter a number.")