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_076/sol1.py

@@ -0,0 +1,55 @@
+"""
+Counting Summations
+Problem 76: https://projecteuler.net/problem=76
+
+It is possible to write five as a sum in exactly six different ways:
+
+4 + 1
+3 + 2
+3 + 1 + 1
+2 + 2 + 1
+2 + 1 + 1 + 1
+1 + 1 + 1 + 1 + 1
+
+How many different ways can one hundred be written as a sum of at least two
+positive integers?
+"""
+
+
+def solution(m: int = 100) -> int:
+    """
+    Returns the number of different ways the number m can be written as a
+    sum of at least two positive integers.
+
+    >>> solution(100)
+    190569291
+    >>> solution(50)
+    204225
+    >>> solution(30)
+    5603
+    >>> solution(10)
+    41
+    >>> solution(5)
+    6
+    >>> solution(3)
+    2
+    >>> solution(2)
+    1
+    >>> solution(1)
+    0
+    """
+    memo = [[0 for _ in range(m)] for _ in range(m + 1)]
+    for i in range(m + 1):
+        memo[i][0] = 1
+
+    for n in range(m + 1):
+        for k in range(1, m):
+            memo[n][k] += memo[n][k - 1]
+            if n > k:
+                memo[n][k] += memo[n - k - 1][k]
+
+    return memo[m][m - 1] - 1
+
+
+if __name__ == "__main__":
+    print(solution(int(input("Enter a number: ").strip())))