From 11e2207182829ee6b1d13c0aec326d5a123d2c9b Mon Sep 17 00:00:00 2001
From: Ankur Chattopadhyay <39518771+chttrjeankr@users.noreply.github.com>
Date: Tue, 22 Oct 2019 21:32:03 +0530
Subject: [PATCH] Project Euler problems 06, 20 (#1419)

* added sol3.py for problem_20

* added sol4.py for problem_06
---
 project_euler/problem_06/sol4.py | 40 ++++++++++++++++++++++++++++++++
 project_euler/problem_20/sol3.py | 39 +++++++++++++++++++++++++++++++
 2 files changed, 79 insertions(+)
 create mode 100644 project_euler/problem_06/sol4.py
 create mode 100644 project_euler/problem_20/sol3.py

diff --git a/project_euler/problem_06/sol4.py b/project_euler/problem_06/sol4.py
new file mode 100644
index 000000000..1e1de5570
--- /dev/null
+++ b/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())))
diff --git a/project_euler/problem_20/sol3.py b/project_euler/problem_20/sol3.py
new file mode 100644
index 000000000..13f9d7831
--- /dev/null
+++ b/project_euler/problem_20/sol3.py
@@ -0,0 +1,39 @@
+"""
+n! means n × (n − 1) × ... × 3 × 2 × 1
+
+For example, 10! = 10 × 9 × ... × 3 × 2 × 1 = 3628800,
+and the sum of the digits in the number 10! is 3 + 6 + 2 + 8 + 8 + 0 + 0 = 27.
+
+Find the sum of the digits in the number 100!
+"""
+from math import factorial
+
+
+def solution(n):
+    """Returns the sum of the digits in the number 100!
+    >>> solution(1000)
+    10539
+    >>> solution(200)
+    1404
+    >>> solution(100)
+    648
+    >>> solution(50)
+    216
+    >>> solution(10)
+    27
+    >>> solution(5)
+    3
+    >>> solution(3)
+    6
+    >>> solution(2)
+    2
+    >>> solution(1)
+    1
+    >>> solution(0)
+    1
+    """
+    return sum(map(int, str(factorial(n))))
+
+
+if __name__ == "__main__":
+    print(solution(int(input("Enter the Number: ").strip())))