Project Euler problems 06, 20 (#1419)

* added sol3.py for problem_20

* added sol4.py for problem_06

project_euler/problem_06/sol4.py

@@ -0,0 +1,40 @@
+# -*- coding: utf-8 -*-
+"""
+Problem:
+
+The sum of the squares of the first ten natural numbers is,
+            1^2 + 2^2 + ... + 10^2 = 385
+
+The square of the sum of the first ten natural numbers is,
+            (1 + 2 + ... + 10)^2 = 552 = 3025
+
+Hence the difference between the sum of the squares of the first ten natural
+numbers and the square of the sum is 3025 − 385 = 2640.
+
+Find the difference between the sum of the squares of the first N natural
+numbers and the square of the sum.
+"""
+
+
+def solution(n):
+    """Returns the difference between the sum of the squares of the first n
+    natural numbers and the square of the sum.
+
+    >>> solution(10)
+    2640
+    >>> solution(15)
+    13160
+    >>> solution(20)
+    41230
+    >>> solution(50)
+    1582700
+    >>> solution(100)
+    25164150
+    """
+    sum_of_squares = n * (n + 1) * (2 * n + 1) / 6
+    square_of_sum = (n * (n + 1) / 2) ** 2
+    return int(square_of_sum - sum_of_squares)
+
+
+if __name__ == "__main__":
+    print(solution(int(input("Enter a number: ").strip())))