Fix style of the first ten solutions for Project Euler (#3242)

* Fix style of the first ten solutions for Project Euler

- Unify the header docstring, and add reference URLs to wikipedia
  or similar
- Fix docstrings to be properly multilined
- Add newlines where appropriate
- Add doctests where they were missing
- Remove doctests that test for the correct solution
- fix obvious spelling or grammar mistakes in comments and
  exception messages
- Fix line endings to be UNIX. This makes two of the files seem
  to have changed completely
- no functional changes in any of the solutions were done
  (except for the spelling fixes mentioned above)

* Fix docstrings and main function as per Style Guide

project_euler/problem_001/sol1.py

 """
-Problem Statement:
+Project Euler Problem 1: https://projecteuler.net/problem=1
+
+Multiples of 3 and 5
+
 If we list all the natural numbers below 10 that are multiples of 3 or 5,
 we get 3, 5, 6 and 9. The sum of these multiples is 23.
-Find the sum of all the multiples of 3 or 5 below N.
+
+Find the sum of all the multiples of 3 or 5 below 1000.
 """
 
 
 def solution(n: int = 1000) -> int:
-    """Returns the sum of all the multiples of 3 or 5 below n.
+    """
+    Returns the sum of all the multiples of 3 or 5 below n.
 
     >>> solution(3)
     0
@@ -25,4 +30,4 @@ def solution(n: int = 1000) -> int:
 
 
 if __name__ == "__main__":
-    print(solution(int(input().strip())))
+    print(f"{solution() = }")

project_euler/problem_001/sol2.py

 """
-Problem Statement:
+Project Euler Problem 1: https://projecteuler.net/problem=1
+
+Multiples of 3 and 5
+
 If we list all the natural numbers below 10 that are multiples of 3 or 5,
 we get 3, 5, 6 and 9. The sum of these multiples is 23.
-Find the sum of all the multiples of 3 or 5 below N.
+
+Find the sum of all the multiples of 3 or 5 below 1000.
 """
 
 
 def solution(n: int = 1000) -> int:
-    """Returns the sum of all the multiples of 3 or 5 below n.
+    """
+    Returns the sum of all the multiples of 3 or 5 below n.
 
     >>> solution(3)
     0
@@ -30,4 +35,4 @@ def solution(n: int = 1000) -> int:
 
 
 if __name__ == "__main__":
-    print(solution(int(input().strip())))
+    print(f"{solution() = }")

project_euler/problem_001/sol3.py

 """
-Problem Statement:
+Project Euler Problem 1: https://projecteuler.net/problem=1
+
+Multiples of 3 and 5
+
 If we list all the natural numbers below 10 that are multiples of 3 or 5,
 we get 3, 5, 6 and 9. The sum of these multiples is 23.
-Find the sum of all the multiples of 3 or 5 below N.
+
+Find the sum of all the multiples of 3 or 5 below 1000.
 """
 
 
@@ -57,4 +61,4 @@ def solution(n: int = 1000) -> int:
 
 
 if __name__ == "__main__":
-    print(solution(int(input().strip())))
+    print(f"{solution() = }")

project_euler/problem_001/sol4.py

-"""
-Problem Statement:
-If we list all the natural numbers below 10 that are multiples of 3 or 5,
-we get 3, 5, 6 and 9. The sum of these multiples is 23.
-Find the sum of all the multiples of 3 or 5 below N.
-"""
-
-
-def solution(n: int = 1000) -> int:
-    """Returns the sum of all the multiples of 3 or 5 below n.
-
-    >>> solution(3)
-    0
-    >>> solution(4)
-    3
-    >>> solution(10)
-    23
-    >>> solution(600)
-    83700
-    """
-
-    xmulti = []
-    zmulti = []
-    z = 3
-    x = 5
-    temp = 1
-    while True:
-        result = z * temp
-        if result < n:
-            zmulti.append(result)
-            temp += 1
-        else:
-            temp = 1
-            break
-    while True:
-        result = x * temp
-        if result < n:
-            xmulti.append(result)
-            temp += 1
-        else:
-            break
-    collection = list(set(xmulti + zmulti))
-    return sum(collection)
-
-
-if __name__ == "__main__":
-    print(solution(int(input().strip())))
+"""
+Project Euler Problem 1: https://projecteuler.net/problem=1
+
+Multiples of 3 and 5
+
+If we list all the natural numbers below 10 that are multiples of 3 or 5,
+we get 3, 5, 6 and 9. The sum of these multiples is 23.
+
+Find the sum of all the multiples of 3 or 5 below 1000.
+"""
+
+
+def solution(n: int = 1000) -> int:
+    """
+    Returns the sum of all the multiples of 3 or 5 below n.
+
+    >>> solution(3)
+    0
+    >>> solution(4)
+    3
+    >>> solution(10)
+    23
+    >>> solution(600)
+    83700
+    """
+
+    xmulti = []
+    zmulti = []
+    z = 3
+    x = 5
+    temp = 1
+    while True:
+        result = z * temp
+        if result < n:
+            zmulti.append(result)
+            temp += 1
+        else:
+            temp = 1
+            break
+    while True:
+        result = x * temp
+        if result < n:
+            xmulti.append(result)
+            temp += 1
+        else:
+            break
+    collection = list(set(xmulti + zmulti))
+    return sum(collection)
+
+
+if __name__ == "__main__":
+    print(f"{solution() = }")

project_euler/problem_001/sol5.py

 """
-Problem Statement:
+Project Euler Problem 1: https://projecteuler.net/problem=1
+
+Multiples of 3 and 5
+
 If we list all the natural numbers below 10 that are multiples of 3 or 5,
 we get 3, 5, 6 and 9. The sum of these multiples is 23.
-Find the sum of all the multiples of 3 or 5 below N.
+
+Find the sum of all the multiples of 3 or 5 below 1000.
 """
 
 
 def solution(n: int = 1000) -> int:
-    """Returns the sum of all the multiples of 3 or 5 below n.
-       A straightforward pythonic solution using list comprehension.
+    """
+    Returns the sum of all the multiples of 3 or 5 below n.
+    A straightforward pythonic solution using list comprehension.
 
     >>> solution(3)
     0
@@ -24,4 +29,4 @@ def solution(n: int = 1000) -> int:
 
 
 if __name__ == "__main__":
-    print(solution(int(input().strip())))
+    print(f"{solution() = }")

project_euler/problem_001/sol6.py

 """
-Problem Statement:
+Project Euler Problem 1: https://projecteuler.net/problem=1
+
+Multiples of 3 and 5
+
 If we list all the natural numbers below 10 that are multiples of 3 or 5,
 we get 3, 5, 6 and 9. The sum of these multiples is 23.
-Find the sum of all the multiples of 3 or 5 below N.
+
+Find the sum of all the multiples of 3 or 5 below 1000.
 """
 
 
 def solution(n: int = 1000) -> int:
-    """Returns the sum of all the multiples of 3 or 5 below n.
+    """
+    Returns the sum of all the multiples of 3 or 5 below n.
 
     >>> solution(3)
     0
@@ -31,4 +36,4 @@ def solution(n: int = 1000) -> int:
 
 
 if __name__ == "__main__":
-    print(solution(int(input().strip())))
+    print(f"{solution() = }")

project_euler/problem_001/sol7.py

 """
-Problem Statement:
+Project Euler Problem 1: https://projecteuler.net/problem=1
+
+Multiples of 3 and 5
+
 If we list all the natural numbers below 10 that are multiples of 3 or 5,
 we get 3, 5, 6 and 9. The sum of these multiples is 23.
-Find the sum of all the multiples of 3 or 5 below N.
+
+Find the sum of all the multiples of 3 or 5 below 1000.
 """
 
 
 def solution(n: int = 1000) -> int:
-    """Returns the sum of all the multiples of 3 or 5 below n.
+    """
+    Returns the sum of all the multiples of 3 or 5 below n.
 
     >>> solution(3)
     0
@@ -29,4 +34,4 @@ def solution(n: int = 1000) -> int:
 
 
 if __name__ == "__main__":
-    print(solution(int(input().strip())))
+    print(f"{solution() = }")

project_euler/problem_002/sol1.py

 """
-Problem:
-Each new term in the Fibonacci sequence is generated by adding the previous two
-terms. By starting with 1 and 2, the first 10 terms will be:
+Project Euler Problem 2: https://projecteuler.net/problem=2
 
-    1,2,3,5,8,13,21,34,55,89,..
+Even Fibonacci Numbers
+
+Each new term in the Fibonacci sequence is generated by adding the previous
+two terms. By starting with 1 and 2, the first 10 terms will be:
+
+1, 2, 3, 5, 8, 13, 21, 34, 55, 89, ...
 
 By considering the terms in the Fibonacci sequence whose values do not exceed
-n, find the sum of the even-valued terms. e.g. for n=10, we have {2,8}, sum is
-10.
+four million, find the sum of the even-valued terms.
+
+References:
+    - https://en.wikipedia.org/wiki/Fibonacci_number
 """
 
 
 def solution(n: int = 4000000) -> int:
-    """Returns the sum of all fibonacci sequence even elements that are lower
-    or equals to n.
+    """
+    Returns the sum of all even fibonacci sequence elements that are lower
+    or equal to n.
 
     >>> solution(10)
     10
@@ -26,6 +32,7 @@ def solution(n: int = 4000000) -> int:
     >>> solution(34)
     44
     """
+
     i = 1
     j = 2
     total = 0
@@ -38,4 +45,4 @@ def solution(n: int = 4000000) -> int:
 
 
 if __name__ == "__main__":
-    print(solution(int(input().strip())))
+    print(f"{solution() = }")

project_euler/problem_002/sol2.py

-"""
-Problem:
-Each new term in the Fibonacci sequence is generated by adding the previous two
-terms. By starting with 1 and 2, the first 10 terms will be:
-
-    1,2,3,5,8,13,21,34,55,89,..
-
-By considering the terms in the Fibonacci sequence whose values do not exceed
-n, find the sum of the even-valued terms. e.g. for n=10, we have {2,8}, sum is
-10.
-"""
-
-
-def solution(n: int = 4000000) -> int:
-    """Returns the sum of all fibonacci sequence even elements that are lower
-    or equals to n.
-
-    >>> solution(10)
-    10
-    >>> solution(15)
-    10
-    >>> solution(2)
-    2
-    >>> solution(1)
-    0
-    >>> solution(34)
-    44
-    """
-    even_fibs = []
-    a, b = 0, 1
-    while b <= n:
-        if b % 2 == 0:
-            even_fibs.append(b)
-        a, b = b, a + b
-    return sum(even_fibs)
-
-
-if __name__ == "__main__":
-    print(solution(int(input().strip())))
+"""
+Project Euler Problem 2: https://projecteuler.net/problem=2
+
+Even Fibonacci Numbers
+
+Each new term in the Fibonacci sequence is generated by adding the previous
+two terms. By starting with 1 and 2, the first 10 terms will be:
+
+1, 2, 3, 5, 8, 13, 21, 34, 55, 89, ...
+
+By considering the terms in the Fibonacci sequence whose values do not exceed
+four million, find the sum of the even-valued terms.
+
+References:
+    - https://en.wikipedia.org/wiki/Fibonacci_number
+"""
+
+
+def solution(n: int = 4000000) -> int:
+    """
+    Returns the sum of all even fibonacci sequence elements that are lower
+    or equal to n.
+
+    >>> solution(10)
+    10
+    >>> solution(15)
+    10
+    >>> solution(2)
+    2
+    >>> solution(1)
+    0
+    >>> solution(34)
+    44
+    """
+
+    even_fibs = []
+    a, b = 0, 1
+    while b <= n:
+        if b % 2 == 0:
+            even_fibs.append(b)
+        a, b = b, a + b
+    return sum(even_fibs)
+
+
+if __name__ == "__main__":
+    print(f"{solution() = }")

project_euler/problem_002/sol3.py

 """
-Problem:
+Project Euler Problem 2: https://projecteuler.net/problem=2
+
+Even Fibonacci Numbers
+
 Each new term in the Fibonacci sequence is generated by adding the previous
 two terms. By starting with 1 and 2, the first 10 terms will be:
 
-    1,2,3,5,8,13,21,34,55,89,..
+1, 2, 3, 5, 8, 13, 21, 34, 55, 89, ...
 
 By considering the terms in the Fibonacci sequence whose values do not exceed
-n, find the sum of the even-valued terms. e.g. for n=10, we have {2,8}, sum is
-10.
+four million, find the sum of the even-valued terms.
+
+References:
+    - https://en.wikipedia.org/wiki/Fibonacci_number
 """
 
 
 def solution(n: int = 4000000) -> int:
-    """Returns the sum of all fibonacci sequence even elements that are lower
-    or equals to n.
+    """
+    Returns the sum of all even fibonacci sequence elements that are lower
+    or equal to n.
 
     >>> solution(10)
     10
@@ -26,6 +32,7 @@ def solution(n: int = 4000000) -> int:
     >>> solution(34)
     44
     """
+
     if n <= 1:
         return 0
     a = 0
@@ -38,4 +45,4 @@ def solution(n: int = 4000000) -> int:
 
 
 if __name__ == "__main__":
-    print(solution(int(input().strip())))
+    print(f"{solution() = }")

project_euler/problem_002/sol4.py

 """
-Problem:
-Each new term in the Fibonacci sequence is generated by adding the previous two
-terms. By starting with 1 and 2, the first 10 terms will be:
+Project Euler Problem 2: https://projecteuler.net/problem=2
 
-    1,2,3,5,8,13,21,34,55,89,..
+Even Fibonacci Numbers
+
+Each new term in the Fibonacci sequence is generated by adding the previous
+two terms. By starting with 1 and 2, the first 10 terms will be:
+
+1, 2, 3, 5, 8, 13, 21, 34, 55, 89, ...
 
 By considering the terms in the Fibonacci sequence whose values do not exceed
-n, find the sum of the even-valued terms. e.g. for n=10, we have {2,8}, sum is
-10.
+four million, find the sum of the even-valued terms.
+
+References:
+    - https://en.wikipedia.org/wiki/Fibonacci_number
 """
 import math
 from decimal import Decimal, getcontext
 
 
 def solution(n: int = 4000000) -> int:
-    """Returns the sum of all fibonacci sequence even elements that are lower
-    or equals to n.
+    """
+    Returns the sum of all even fibonacci sequence elements that are lower
+    or equal to n.
 
     >>> solution(10)
     10
@@ -32,26 +38,27 @@ def solution(n: int = 4000000) -> int:
     >>> solution(0)
     Traceback (most recent call last):
         ...
-    ValueError: Parameter n must be greater or equal to one.
+    ValueError: Parameter n must be greater than or equal to one.
     >>> solution(-17)
     Traceback (most recent call last):
         ...
-    ValueError: Parameter n must be greater or equal to one.
+    ValueError: Parameter n must be greater than or equal to one.
     >>> solution([])
     Traceback (most recent call last):
         ...
-    TypeError: Parameter n must be int or passive of cast to int.
+    TypeError: Parameter n must be int or castable to int.
     >>> solution("asd")
     Traceback (most recent call last):
         ...
-    TypeError: Parameter n must be int or passive of cast to int.
+    TypeError: Parameter n must be int or castable to int.
     """
+
     try:
         n = int(n)
     except (TypeError, ValueError):
-        raise TypeError("Parameter n must be int or passive of cast to int.")
+        raise TypeError("Parameter n must be int or castable to int.")
     if n <= 0:
-        raise ValueError("Parameter n must be greater or equal to one.")
+        raise ValueError("Parameter n must be greater than or equal to one.")
     getcontext().prec = 100
     phi = (Decimal(5) ** Decimal(0.5) + 1) / Decimal(2)
 
@@ -62,4 +69,4 @@ def solution(n: int = 4000000) -> int:
 
 
 if __name__ == "__main__":
-    print(solution(int(input().strip())))
+    print(f"{solution() = }")

project_euler/problem_002/sol5.py

 """
-Problem:
-Each new term in the Fibonacci sequence is generated by adding the previous two
-terms. By starting with 1 and 2, the first 10 terms will be:
+Project Euler Problem 2: https://projecteuler.net/problem=2
 
-    1,2,3,5,8,13,21,34,55,89,..
+Even Fibonacci Numbers
+
+Each new term in the Fibonacci sequence is generated by adding the previous
+two terms. By starting with 1 and 2, the first 10 terms will be:
+
+1, 2, 3, 5, 8, 13, 21, 34, 55, 89, ...
 
 By considering the terms in the Fibonacci sequence whose values do not exceed
-n, find the sum of the even-valued terms. e.g. for n=10, we have {2,8}, sum is
-10.
+four million, find the sum of the even-valued terms.
+
+References:
+    - https://en.wikipedia.org/wiki/Fibonacci_number
 """
 
 
 def solution(n: int = 4000000) -> int:
-    """Returns the sum of all fibonacci sequence even elements that are lower
-    or equals to n.
+    """
+    Returns the sum of all even fibonacci sequence elements that are lower
+    or equal to n.
 
     >>> solution(10)
     10
@@ -43,4 +49,4 @@ def solution(n: int = 4000000) -> int:
 
 
 if __name__ == "__main__":
-    print(solution(int(input().strip())))
+    print(f"{solution() = }")

project_euler/problem_003/sol1.py

 """
-Problem:
-The prime factors of 13195 are 5,7,13 and 29. What is the largest prime factor
-of a given number N?
+Project Euler Problem 3: https://projecteuler.net/problem=3
 
-e.g. for 10, largest prime factor = 5. For 17, largest prime factor = 17.
-"""
+Largest prime factor
+
+The prime factors of 13195 are 5, 7, 13 and 29.
+
+What is the largest prime factor of the number 600851475143?
 
+References:
+    - https://en.wikipedia.org/wiki/Prime_number#Unique_factorization
+"""
 import math
 
 
 def isprime(num: int) -> bool:
-    """Returns boolean representing primality of given number num.
+    """
+    Returns boolean representing primality of given number num.
+
     >>> isprime(2)
     True
     >>> isprime(3)
@@ -22,14 +28,15 @@ def isprime(num: int) -> bool:
     >>> isprime(0)
     Traceback (most recent call last):
         ...
-    ValueError: Parameter num must be greater or equal to two.
+    ValueError: Parameter num must be greater than or equal to two.
     >>> isprime(1)
     Traceback (most recent call last):
         ...
-    ValueError: Parameter num must be greater or equal to two.
+    ValueError: Parameter num must be greater than or equal to two.
     """
+
     if num <= 1:
-        raise ValueError("Parameter num must be greater or equal to two.")
+        raise ValueError("Parameter num must be greater than or equal to two.")
     if num == 2:
         return True
     elif num % 2 == 0:
@@ -41,7 +48,9 @@ def isprime(num: int) -> bool:
 
 
 def solution(n: int = 600851475143) -> int:
-    """Returns the largest prime factor of a given number n.
+    """
+    Returns the largest prime factor of a given number n.
+
     >>> solution(13195)
     29
     >>> solution(10)
@@ -53,26 +62,27 @@ def solution(n: int = 600851475143) -> int:
     >>> solution(0)
     Traceback (most recent call last):
         ...
-    ValueError: Parameter n must be greater or equal to one.
+    ValueError: Parameter n must be greater than or equal to one.
     >>> solution(-17)
     Traceback (most recent call last):
         ...
-    ValueError: Parameter n must be greater or equal to one.
+    ValueError: Parameter n must be greater than or equal to one.
     >>> solution([])
     Traceback (most recent call last):
         ...
-    TypeError: Parameter n must be int or passive of cast to int.
+    TypeError: Parameter n must be int or castable to int.
     >>> solution("asd")
     Traceback (most recent call last):
         ...
-    TypeError: Parameter n must be int or passive of cast to int.
+    TypeError: Parameter n must be int or castable to int.
     """
+
     try:
         n = int(n)
     except (TypeError, ValueError):
-        raise TypeError("Parameter n must be int or passive of cast to int.")
+        raise TypeError("Parameter n must be int or castable to int.")
     if n <= 0:
-        raise ValueError("Parameter n must be greater or equal to one.")
+        raise ValueError("Parameter n must be greater than or equal to one.")
     max_number = 0
     if isprime(n):
         return n
@@ -91,4 +101,4 @@ def solution(n: int = 600851475143) -> int:
 
 
 if __name__ == "__main__":
-    print(solution(int(input().strip())))
+    print(f"{solution() = }")

project_euler/problem_003/sol2.py

 """
-Problem:
-The prime factors of 13195 are 5,7,13 and 29. What is the largest prime factor
-of a given number N?
+Project Euler Problem 3: https://projecteuler.net/problem=3
 
-e.g. for 10, largest prime factor = 5. For 17, largest prime factor = 17.
+Largest prime factor
+
+The prime factors of 13195 are 5, 7, 13 and 29.
+
+What is the largest prime factor of the number 600851475143?
+
+References:
+    - https://en.wikipedia.org/wiki/Prime_number#Unique_factorization
 """
 
 
 def solution(n: int = 600851475143) -> int:
-    """Returns the largest prime factor of a given number n.
+    """
+    Returns the largest prime factor of a given number n.
+
     >>> solution(13195)
     29
     >>> solution(10)
@@ -20,26 +27,27 @@ def solution(n: int = 600851475143) -> int:
     >>> solution(0)
     Traceback (most recent call last):
         ...
-    ValueError: Parameter n must be greater or equal to one.
+    ValueError: Parameter n must be greater than or equal to one.
     >>> solution(-17)
     Traceback (most recent call last):
         ...
-    ValueError: Parameter n must be greater or equal to one.
+    ValueError: Parameter n must be greater than or equal to one.
     >>> solution([])
     Traceback (most recent call last):
         ...
-    TypeError: Parameter n must be int or passive of cast to int.
+    TypeError: Parameter n must be int or castable to int.
     >>> solution("asd")
     Traceback (most recent call last):
         ...
-    TypeError: Parameter n must be int or passive of cast to int.
+    TypeError: Parameter n must be int or castable to int.
     """
+
     try:
         n = int(n)
     except (TypeError, ValueError):
-        raise TypeError("Parameter n must be int or passive of cast to int.")
+        raise TypeError("Parameter n must be int or castable to int.")
     if n <= 0:
-        raise ValueError("Parameter n must be greater or equal to one.")
+        raise ValueError("Parameter n must be greater than or equal to one.")
     prime = 1
     i = 2
     while i * i <= n:
@@ -53,4 +61,4 @@ def solution(n: int = 600851475143) -> int:
 
 
 if __name__ == "__main__":
-    print(solution(int(input().strip())))
+    print(f"{solution() = }")

project_euler/problem_003/sol3.py

 """
-Problem:
-The prime factors of 13195 are 5,7,13 and 29. What is the largest prime factor
-of a given number N?
+Project Euler Problem 3: https://projecteuler.net/problem=3
 
-e.g. for 10, largest prime factor = 5. For 17, largest prime factor = 17.
+Largest prime factor
+
+The prime factors of 13195 are 5, 7, 13 and 29.
+
+What is the largest prime factor of the number 600851475143?
+
+References:
+    - https://en.wikipedia.org/wiki/Prime_number#Unique_factorization
 """
 
 
 def solution(n: int = 600851475143) -> int:
-    """Returns the largest prime factor of a given number n.
+    """
+    Returns the largest prime factor of a given number n.
+
     >>> solution(13195)
     29
     >>> solution(10)
@@ -20,26 +27,27 @@ def solution(n: int = 600851475143) -> int:
     >>> solution(0)
     Traceback (most recent call last):
         ...
-    ValueError: Parameter n must be greater or equal to one.
+    ValueError: Parameter n must be greater than or equal to one.
     >>> solution(-17)
     Traceback (most recent call last):
         ...
-    ValueError: Parameter n must be greater or equal to one.
+    ValueError: Parameter n must be greater than or equal to one.
     >>> solution([])
     Traceback (most recent call last):
         ...
-    TypeError: Parameter n must be int or passive of cast to int.
+    TypeError: Parameter n must be int or castable to int.
     >>> solution("asd")
     Traceback (most recent call last):
         ...
-    TypeError: Parameter n must be int or passive of cast to int.
+    TypeError: Parameter n must be int or castable to int.
     """
+
     try:
         n = int(n)
     except (TypeError, ValueError):
-        raise TypeError("Parameter n must be int or passive of cast to int.")
+        raise TypeError("Parameter n must be int or castable to int.")
     if n <= 0:
-        raise ValueError("Parameter n must be greater or equal to one.")
+        raise ValueError("Parameter n must be greater than or equal to one.")
     i = 2
     ans = 0
     if n == 2:
@@ -55,4 +63,4 @@ def solution(n: int = 600851475143) -> int:
 
 
 if __name__ == "__main__":
-    print(solution(int(input().strip())))
+    print(f"{solution() = }")

project_euler/problem_004/sol1.py

 """
-Problem:
-A palindromic number reads the same both ways. The largest palindrome made from
-the product of two 2-digit numbers is 9009 = 91 x 99.
+Project Euler Problem 4: https://projecteuler.net/problem=4
 
-Find the largest palindrome made from the product of two 3-digit numbers which
-is less than N.
+Largest palindrome product
+
+A palindromic number reads the same both ways. The largest palindrome made
+from the product of two 2-digit numbers is 9009 = 91 × 99.
+
+Find the largest palindrome made from the product of two 3-digit numbers.
+
+References:
+    - https://en.wikipedia.org/wiki/Palindromic_number
 """
 
 
 def solution(n: int = 998001) -> int:
-    """Returns the largest palindrome made from the product of two 3-digit
+    """
+    Returns the largest palindrome made from the product of two 3-digit
     numbers which is less than n.
 
     >>> solution(20000)
@@ -23,10 +29,10 @@ def solution(n: int = 998001) -> int:
     ...
     ValueError: That number is larger than our acceptable range.
     """
+
     # fetches the next number
     for number in range(n - 1, 9999, -1):
 
-        # converts number into string.
         str_number = str(number)
 
         # checks whether 'str_number' is a palindrome.
@@ -44,8 +50,4 @@ def solution(n: int = 998001) -> int:
 
 
 if __name__ == "__main__":
-    import doctest
-
-    doctest.testmod()
-
-    print(solution(int(input().strip())))
+    print(f"{solution() = }")

project_euler/problem_004/sol2.py

 """
-Problem:
-A palindromic number reads the same both ways. The largest palindrome made from
-the product of two 2-digit numbers is 9009 = 91 x 99.
+Project Euler Problem 4: https://projecteuler.net/problem=4
 
-Find the largest palindrome made from the product of two 3-digit numbers which
-is less than N.
+Largest palindrome product
+
+A palindromic number reads the same both ways. The largest palindrome made
+from the product of two 2-digit numbers is 9009 = 91 × 99.
+
+Find the largest palindrome made from the product of two 3-digit numbers.
+
+References:
+    - https://en.wikipedia.org/wiki/Palindromic_number
 """
 
 
 def solution(n: int = 998001) -> int:
-    """Returns the largest palindrome made from the product of two 3-digit
+    """
+    Returns the largest palindrome made from the product of two 3-digit
     numbers which is less than n.
 
     >>> solution(20000)
@@ -19,6 +25,7 @@ def solution(n: int = 998001) -> int:
     >>> solution(40000)
     39893
     """
+
     answer = 0
     for i in range(999, 99, -1):  # 3 digit numbers range from 999 down to 100
         for j in range(999, 99, -1):
@@ -29,4 +36,4 @@ def solution(n: int = 998001) -> int:
 
 
 if __name__ == "__main__":
-    print(solution(int(input().strip())))
+    print(f"{solution() = }")

project_euler/problem_005/sol1.py

 """
-Problem:
-2520 is the smallest number that can be divided by each of the numbers from 1
-to 10 without any remainder.
+Project Euler Problem 5: https://projecteuler.net/problem=5
 
-What is the smallest positive number that is evenly divisible(divisible with no
-remainder) by all of the numbers from 1 to N?
+Smallest multiple
+
+2520 is the smallest number that can be divided by each of the numbers
+from 1 to 10 without any remainder.
+
+What is the smallest positive number that is _evenly divisible_ by all
+of the numbers from 1 to 20?
+
+References:
+    - https://en.wiktionary.org/wiki/evenly_divisible
 """
 
 
 def solution(n: int = 20) -> int:
-    """Returns the smallest positive number that is evenly divisible(divisible
+    """
+    Returns the smallest positive number that is evenly divisible (divisible
     with no remainder) by all of the numbers from 1 to n.
 
     >>> solution(10)
     2520
     >>> solution(15)
     360360
-    >>> solution(20)
-    232792560
     >>> solution(22)
     232792560
     >>> solution(3.4)
@@ -25,26 +30,27 @@ def solution(n: int = 20) -> int:
     >>> solution(0)
     Traceback (most recent call last):
         ...
-    ValueError: Parameter n must be greater or equal to one.
+    ValueError: Parameter n must be greater than or equal to one.
     >>> solution(-17)
     Traceback (most recent call last):
         ...
-    ValueError: Parameter n must be greater or equal to one.
+    ValueError: Parameter n must be greater than or equal to one.
     >>> solution([])
     Traceback (most recent call last):
         ...
-    TypeError: Parameter n must be int or passive of cast to int.
+    TypeError: Parameter n must be int or castable to int.
     >>> solution("asd")
     Traceback (most recent call last):
         ...
-    TypeError: Parameter n must be int or passive of cast to int.
+    TypeError: Parameter n must be int or castable to int.
     """
+
     try:
         n = int(n)
     except (TypeError, ValueError):
-        raise TypeError("Parameter n must be int or passive of cast to int.")
+        raise TypeError("Parameter n must be int or castable to int.")
     if n <= 0:
-        raise ValueError("Parameter n must be greater or equal to one.")
+        raise ValueError("Parameter n must be greater than or equal to one.")
     i = 0
     while 1:
         i += n * (n - 1)
@@ -60,4 +66,4 @@ def solution(n: int = 20) -> int:
 
 
 if __name__ == "__main__":
-    print(solution(int(input().strip())))
+    print(f"{solution() = }")

project_euler/problem_005/sol2.py

 """
-Problem:
-2520 is the smallest number that can be divided by each of the numbers from 1
-to 10 without any remainder.
+Project Euler Problem 5: https://projecteuler.net/problem=5
 
-What is the smallest positive number that is evenly divisible(divisible with no
-remainder) by all of the numbers from 1 to N?
+Smallest multiple
+
+2520 is the smallest number that can be divided by each of the numbers
+from 1 to 10 without any remainder.
+
+What is the smallest positive number that is _evenly divisible_ by all
+of the numbers from 1 to 20?
+
+References:
+    - https://en.wiktionary.org/wiki/evenly_divisible
+    - https://en.wikipedia.org/wiki/Euclidean_algorithm
+    - https://en.wikipedia.org/wiki/Least_common_multiple
 """
-""" Euclidean GCD Algorithm """
 
 
 def gcd(x: int, y: int) -> int:
-    return x if y == 0 else gcd(y, x % y)
+    """
+    Euclidean GCD algorithm (Greatest Common Divisor)
 
+    >>> gcd(0, 0)
+    0
+    >>> gcd(23, 42)
+    1
+    >>> gcd(15, 33)
+    3
+    >>> gcd(12345, 67890)
+    15
+    """
 
-""" Using the property lcm*gcd of two numbers = product of them """
+    return x if y == 0 else gcd(y, x % y)
 
 
 def lcm(x: int, y: int) -> int:
+    """
+    Least Common Multiple.
+
+    Using the property that lcm(a, b) * gcd(a, b) = a*b
+
+    >>> lcm(3, 15)
+    15
+    >>> lcm(1, 27)
+    27
+    >>> lcm(13, 27)
+    351
+    >>> lcm(64, 48)
+    192
+    """
+
     return (x * y) // gcd(x, y)
 
 
 def solution(n: int = 20) -> int:
-    """Returns the smallest positive number that is evenly divisible(divisible
+    """
+    Returns the smallest positive number that is evenly divisible (divisible
     with no remainder) by all of the numbers from 1 to n.
 
     >>> solution(10)
     2520
     >>> solution(15)
     360360
-    >>> solution(20)
-    232792560
     >>> solution(22)
     232792560
     """
+
     g = 1
     for i in range(1, n + 1):
         g = lcm(g, i)
@@ -40,4 +72,4 @@ def solution(n: int = 20) -> int:
 
 
 if __name__ == "__main__":
-    print(solution(int(input().strip())))
+    print(f"{solution() = }")

project_euler/problem_006/sol1.py

 """
-Problem 6: https://projecteuler.net/problem=6
+Project Euler Problem 6: https://projecteuler.net/problem=6
+
+Sum square difference
 
 The sum of the squares of the first ten natural numbers is,
-            1^2 + 2^2 + ... + 10^2 = 385
+    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
+    (1 + 2 + ... + 10)^2 = 55^2 = 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.
+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.
+Find the difference between the sum of the squares of the first one
+hundred natural numbers and the square of the sum.
 """
 
 
 def solution(n: int = 100) -> int:
-    """Returns the difference between the sum of the squares of the first n
+    """
+    Returns the difference between the sum of the squares of the first n
     natural numbers and the square of the sum.
 
     >>> solution(10)
@@ -27,9 +30,8 @@ def solution(n: int = 100) -> int:
     41230
     >>> solution(50)
     1582700
-    >>> solution()
-    25164150
     """
+
     sum_of_squares = 0
     sum_of_ints = 0
     for i in range(1, n + 1):
@@ -39,7 +41,4 @@ def solution(n: int = 100) -> int:
 
 
 if __name__ == "__main__":
-    import doctest
-
-    doctest.testmod()
-    print(solution(int(input().strip())))
+    print(f"{solution() = }")

project_euler/problem_006/sol2.py

 """
-Problem 6: https://projecteuler.net/problem=6
+Project Euler Problem 6: https://projecteuler.net/problem=6
+
+Sum square difference
 
 The sum of the squares of the first ten natural numbers is,
-            1^2 + 2^2 + ... + 10^2 = 385
+    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
+    (1 + 2 + ... + 10)^2 = 55^2 = 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.
+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.
+Find the difference between the sum of the squares of the first one
+hundred natural numbers and the square of the sum.
 """
 
 
 def solution(n: int = 100) -> int:
-    """Returns the difference between the sum of the squares of the first n
+    """
+    Returns the difference between the sum of the squares of the first n
     natural numbers and the square of the sum.
 
     >>> solution(10)
@@ -27,16 +30,12 @@ def solution(n: int = 100) -> int:
     41230
     >>> solution(50)
     1582700
-    >>> solution()
-    25164150
     """
+
     sum_cubes = (n * (n + 1) // 2) ** 2
     sum_squares = n * (n + 1) * (2 * n + 1) // 6
     return sum_cubes - sum_squares
 
 
 if __name__ == "__main__":
-    import doctest
-
-    doctest.testmod()
-    print(solution(int(input().strip())))
+    print(f"{solution() = }")

project_euler/problem_006/sol3.py

 """
-Problem 6: https://projecteuler.net/problem=6
+Project Euler Problem 6: https://projecteuler.net/problem=6
+
+Sum square difference
 
 The sum of the squares of the first ten natural numbers is,
-            1^2 + 2^2 + ... + 10^2 = 385
+    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
+    (1 + 2 + ... + 10)^2 = 55^2 = 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.
+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.
+Find the difference between the sum of the squares of the first one
+hundred natural numbers and the square of the sum.
 """
 import math
 
 
 def solution(n: int = 100) -> int:
-    """Returns the difference between the sum of the squares of the first n
+    """
+    Returns the difference between the sum of the squares of the first n
     natural numbers and the square of the sum.
 
     >>> solution(10)
@@ -28,16 +31,12 @@ def solution(n: int = 100) -> int:
     41230
     >>> solution(50)
     1582700
-    >>> solution()
-    25164150
     """
+
     sum_of_squares = sum([i * i for i in range(1, n + 1)])
     square_of_sum = int(math.pow(sum(range(1, n + 1)), 2))
     return square_of_sum - sum_of_squares
 
 
 if __name__ == "__main__":
-    import doctest
-
-    doctest.testmod()
-    print(solution(int(input().strip())))
+    print(f"{solution() = }")

project_euler/problem_006/sol4.py

 """
-Problem 6: https://projecteuler.net/problem=6
+Project Euler Problem 6: https://projecteuler.net/problem=6
+
+Sum square difference
 
 The sum of the squares of the first ten natural numbers is,
-            1^2 + 2^2 + ... + 10^2 = 385
+    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
+    (1 + 2 + ... + 10)^2 = 55^2 = 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.
+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.
+Find the difference between the sum of the squares of the first one
+hundred natural numbers and the square of the sum.
 """
 
 
 def solution(n: int = 100) -> int:
-    """Returns the difference between the sum of the squares of the first n
+    """
+    Returns the difference between the sum of the squares of the first n
     natural numbers and the square of the sum.
 
     >>> solution(10)
@@ -27,16 +30,12 @@ def solution(n: int = 100) -> int:
     41230
     >>> solution(50)
     1582700
-    >>> solution()
-    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__":
-    import doctest
-
-    doctest.testmod()
-    print(solution(int(input("Enter a number: ").strip())))
+    print(f"{solution() = }")

project_euler/problem_007/sol1.py

 """
-Problem 7: https://projecteuler.net/problem=7
+Project Euler Problem 7: https://projecteuler.net/problem=7
 
-By listing the first six prime numbers:
+10001st prime
 
-    2, 3, 5, 7, 11, and 13
+By listing the first six prime numbers: 2, 3, 5, 7, 11, and 13, we
+can see that the 6th prime is 13.
 
-We can see that the 6th prime is 13. What is the Nth prime number?
+What is the 10001st prime number?
+
+References:
+    - https://en.wikipedia.org/wiki/Prime_number
 """
+
 from math import sqrt
 
 
 def is_prime(num: int) -> bool:
-    """Determines whether the given number is prime or not"""
+    """
+    Determines whether the given number is prime or not
+
+    >>> is_prime(2)
+    True
+    >>> is_prime(15)
+    False
+    >>> is_prime(29)
+    True
+    >>> is_prime(0)
+    False
+    """
+
     if num == 2:
         return True
     elif num % 2 == 0:
@@ -25,7 +42,8 @@ def is_prime(num: int) -> bool:
 
 
 def solution(nth: int = 10001) -> int:
-    """Returns the n-th prime number.
+    """
+    Returns the n-th prime number.
 
     >>> solution(6)
     13
@@ -39,9 +57,8 @@ def solution(nth: int = 10001) -> int:
     229
     >>> solution(100)
     541
-    >>> solution()
-    104743
     """
+
     count = 0
     number = 1
     while count != nth and number < 3:
@@ -56,4 +73,4 @@ def solution(nth: int = 10001) -> int:
 
 
 if __name__ == "__main__":
-    print(solution(int(input().strip())))
+    print(f"{solution() = }")

project_euler/problem_007/sol2.py

 """
-Problem 7: https://projecteuler.net/problem=7
+Project Euler Problem 7: https://projecteuler.net/problem=7
 
-By listing the first six prime numbers:
+10001st prime
 
-    2, 3, 5, 7, 11, and 13
+By listing the first six prime numbers: 2, 3, 5, 7, 11, and 13, we
+can see that the 6th prime is 13.
 
-We can see that the 6th prime is 13. What is the Nth prime number?
+What is the 10001st prime number?
+
+References:
+    - https://en.wikipedia.org/wiki/Prime_number
 """
 
 
 def isprime(number: int) -> bool:
-    """Determines whether the given number is prime or not"""
+    """
+    Determines whether the given number is prime or not
+
+    >>> isprime(2)
+    True
+    >>> isprime(15)
+    False
+    >>> isprime(29)
+    True
+    """
+
     for i in range(2, int(number ** 0.5) + 1):
         if number % i == 0:
             return False
@@ -18,7 +32,8 @@ def isprime(number: int) -> bool:
 
 
 def solution(nth: int = 10001) -> int:
-    """Returns the n-th prime number.
+    """
+    Returns the n-th prime number.
 
     >>> solution(6)
     13
@@ -32,35 +47,32 @@ def solution(nth: int = 10001) -> int:
     229
     >>> solution(100)
     541
-    >>> solution()
-    104743
     >>> solution(3.4)
     5
     >>> solution(0)
     Traceback (most recent call last):
         ...
-    ValueError: Parameter nth must be greater or equal to one.
+    ValueError: Parameter nth must be greater than or equal to one.
     >>> solution(-17)
     Traceback (most recent call last):
         ...
-    ValueError: Parameter nth must be greater or equal to one.
+    ValueError: Parameter nth must be greater than or equal to one.
     >>> solution([])
     Traceback (most recent call last):
         ...
-    TypeError: Parameter nth must be int or passive of cast to int.
+    TypeError: Parameter nth must be int or castable to int.
     >>> solution("asd")
     Traceback (most recent call last):
         ...
-    TypeError: Parameter nth must be int or passive of cast to int.
+    TypeError: Parameter nth must be int or castable to int.
     """
+
     try:
         nth = int(nth)
     except (TypeError, ValueError):
-        raise TypeError(
-            "Parameter nth must be int or passive of cast to int."
-        ) from None
+        raise TypeError("Parameter nth must be int or castable to int.") from None
     if nth <= 0:
-        raise ValueError("Parameter nth must be greater or equal to one.")
+        raise ValueError("Parameter nth must be greater than or equal to one.")
     primes = []
     num = 2
     while len(primes) < nth:
@@ -73,4 +85,4 @@ def solution(nth: int = 10001) -> int:
 
 
 if __name__ == "__main__":
-    print(solution(int(input().strip())))
+    print(f"{solution() = }")

project_euler/problem_007/sol3.py

 """
-Project 7: https://projecteuler.net/problem=7
+Project Euler Problem 7: https://projecteuler.net/problem=7
 
-By listing the first six prime numbers:
+10001st prime
 
-    2, 3, 5, 7, 11, and 13
+By listing the first six prime numbers: 2, 3, 5, 7, 11, and 13, we
+can see that the 6th prime is 13.
 
-We can see that the 6th prime is 13. What is the Nth prime number?
+What is the 10001st prime number?
+
+References:
+    - https://en.wikipedia.org/wiki/Prime_number
 """
 import itertools
 import math
 
 
 def prime_check(number: int) -> bool:
-    """Determines whether a given number is prime or not"""
+    """
+    Determines whether a given number is prime or not
+
+    >>> prime_check(2)
+    True
+    >>> prime_check(15)
+    False
+    >>> prime_check(29)
+    True
+    """
+
     if number % 2 == 0 and number > 2:
         return False
     return all(number % i for i in range(3, int(math.sqrt(number)) + 1, 2))
 
 
 def prime_generator():
+    """
+    Generate a sequence of prime numbers
+    """
+
     num = 2
     while True:
         if prime_check(num):
@@ -27,7 +45,8 @@ def prime_generator():
 
 
 def solution(nth: int = 10001) -> int:
-    """Returns the n-th prime number.
+    """
+    Returns the n-th prime number.
 
     >>> solution(6)
     13
@@ -41,11 +60,9 @@ def solution(nth: int = 10001) -> int:
     229
     >>> solution(100)
     541
-    >>> solution()
-    104743
     """
     return next(itertools.islice(prime_generator(), nth - 1, nth))
 
 
 if __name__ == "__main__":
-    print(solution(int(input().strip())))
+    print(f"{solution() = }")

project_euler/problem_008/sol1.py

 """
-Problem 8: https://projecteuler.net/problem=8
+Project Euler Problem 8: https://projecteuler.net/problem=8
+
+Largest product in a series
 
 The four adjacent digits in the 1000-digit number that have the greatest
 product are 9 × 9 × 8 × 9 = 5832.
 
-73167176531330624919225119674426574742355349194934
-96983520312774506326239578318016984801869478851843
-85861560789112949495459501737958331952853208805511
-12540698747158523863050715693290963295227443043557
-66896648950445244523161731856403098711121722383113
-62229893423380308135336276614282806444486645238749
-30358907296290491560440772390713810515859307960866
-70172427121883998797908792274921901699720888093776
-65727333001053367881220235421809751254540594752243
-52584907711670556013604839586446706324415722155397
-53697817977846174064955149290862569321978468622482
-83972241375657056057490261407972968652414535100474
-82166370484403199890008895243450658541227588666881
-16427171479924442928230863465674813919123162824586
-17866458359124566529476545682848912883142607690042
-24219022671055626321111109370544217506941658960408
-07198403850962455444362981230987879927244284909188
-84580156166097919133875499200524063689912560717606
-05886116467109405077541002256983155200055935729725
-71636269561882670428252483600823257530420752963450
+    73167176531330624919225119674426574742355349194934
+    96983520312774506326239578318016984801869478851843
+    85861560789112949495459501737958331952853208805511
+    12540698747158523863050715693290963295227443043557
+    66896648950445244523161731856403098711121722383113
+    62229893423380308135336276614282806444486645238749
+    30358907296290491560440772390713810515859307960866
+    70172427121883998797908792274921901699720888093776
+    65727333001053367881220235421809751254540594752243
+    52584907711670556013604839586446706324415722155397
+    53697817977846174064955149290862569321978468622482
+    83972241375657056057490261407972968652414535100474
+    82166370484403199890008895243450658541227588666881
+    16427171479924442928230863465674813919123162824586
+    17866458359124566529476545682848912883142607690042
+    24219022671055626321111109370544217506941658960408
+    07198403850962455444362981230987879927244284909188
+    84580156166097919133875499200524063689912560717606
+    05886116467109405077541002256983155200055935729725
+    71636269561882670428252483600823257530420752963450
 
 Find the thirteen adjacent digits in the 1000-digit number that have the
 greatest product. What is the value of this product?
 """
+
 import sys
 
 N = """73167176531330624919225119674426574742355349194934\
@@ -53,12 +56,18 @@ N = """73167176531330624919225119674426574742355349194934\
 
 
 def solution(n: str = N) -> int:
-    """Find the thirteen adjacent digits in the 1000-digit number n that have
+    """
+    Find the thirteen adjacent digits in the 1000-digit number n that have
     the greatest product and returns it.
 
-    >>> solution(N)
-    23514624000
+    >>> solution("13978431290823798458352374")
+    609638400
+    >>> solution("13978431295823798458352374")
+    2612736000
+    >>> solution("1397843129582379841238352374")
+    209018880
     """
+
     largest_product = -sys.maxsize - 1
     for i in range(len(n) - 12):
         product = 1
@@ -70,4 +79,4 @@ def solution(n: str = N) -> int:
 
 
 if __name__ == "__main__":
-    print(solution(N))
+    print(f"{solution() = }")

project_euler/problem_008/sol2.py

 """
-Problem 8: https://projecteuler.net/problem=8
+Project Euler Problem 8: https://projecteuler.net/problem=8
+
+Largest product in a series
 
 The four adjacent digits in the 1000-digit number that have the greatest
 product are 9 × 9 × 8 × 9 = 5832.
 
-73167176531330624919225119674426574742355349194934
-96983520312774506326239578318016984801869478851843
-85861560789112949495459501737958331952853208805511
-12540698747158523863050715693290963295227443043557
-66896648950445244523161731856403098711121722383113
-62229893423380308135336276614282806444486645238749
-30358907296290491560440772390713810515859307960866
-70172427121883998797908792274921901699720888093776
-65727333001053367881220235421809751254540594752243
-52584907711670556013604839586446706324415722155397
-53697817977846174064955149290862569321978468622482
-83972241375657056057490261407972968652414535100474
-82166370484403199890008895243450658541227588666881
-16427171479924442928230863465674813919123162824586
-17866458359124566529476545682848912883142607690042
-24219022671055626321111109370544217506941658960408
-07198403850962455444362981230987879927244284909188
-84580156166097919133875499200524063689912560717606
-05886116467109405077541002256983155200055935729725
-71636269561882670428252483600823257530420752963450
+    73167176531330624919225119674426574742355349194934
+    96983520312774506326239578318016984801869478851843
+    85861560789112949495459501737958331952853208805511
+    12540698747158523863050715693290963295227443043557
+    66896648950445244523161731856403098711121722383113
+    62229893423380308135336276614282806444486645238749
+    30358907296290491560440772390713810515859307960866
+    70172427121883998797908792274921901699720888093776
+    65727333001053367881220235421809751254540594752243
+    52584907711670556013604839586446706324415722155397
+    53697817977846174064955149290862569321978468622482
+    83972241375657056057490261407972968652414535100474
+    82166370484403199890008895243450658541227588666881
+    16427171479924442928230863465674813919123162824586
+    17866458359124566529476545682848912883142607690042
+    24219022671055626321111109370544217506941658960408
+    07198403850962455444362981230987879927244284909188
+    84580156166097919133875499200524063689912560717606
+    05886116467109405077541002256983155200055935729725
+    71636269561882670428252483600823257530420752963450
 
 Find the thirteen adjacent digits in the 1000-digit number that have the
 greatest product. What is the value of this product?
 """
-
 from functools import reduce
 
 N = (
@@ -56,12 +57,18 @@ N = (
 
 
 def solution(n: str = N) -> int:
-    """Find the thirteen adjacent digits in the 1000-digit number n that have
+    """
+    Find the thirteen adjacent digits in the 1000-digit number n that have
     the greatest product and returns it.
 
-    >>> solution(N)
-    23514624000
+    >>> solution("13978431290823798458352374")
+    609638400
+    >>> solution("13978431295823798458352374")
+    2612736000
+    >>> solution("1397843129582379841238352374")
+    209018880
     """
+
     return max(
         [
             reduce(lambda x, y: int(x) * int(y), n[i : i + 13])
@@ -71,4 +78,4 @@ def solution(n: str = N) -> int:
 
 
 if __name__ == "__main__":
-    print(solution(str(N)))
+    print(f"{solution() = }")

project_euler/problem_008/sol3.py

 """
-Problem 8: https://projecteuler.net/problem=8
+Project Euler Problem 8: https://projecteuler.net/problem=8
+
+Largest product in a series
 
 The four adjacent digits in the 1000-digit number that have the greatest
 product are 9 × 9 × 8 × 9 = 5832.
 
-73167176531330624919225119674426574742355349194934
-96983520312774506326239578318016984801869478851843
-85861560789112949495459501737958331952853208805511
-12540698747158523863050715693290963295227443043557
-66896648950445244523161731856403098711121722383113
-62229893423380308135336276614282806444486645238749
-30358907296290491560440772390713810515859307960866
-70172427121883998797908792274921901699720888093776
-65727333001053367881220235421809751254540594752243
-52584907711670556013604839586446706324415722155397
-53697817977846174064955149290862569321978468622482
-83972241375657056057490261407972968652414535100474
-82166370484403199890008895243450658541227588666881
-16427171479924442928230863465674813919123162824586
-17866458359124566529476545682848912883142607690042
-24219022671055626321111109370544217506941658960408
-07198403850962455444362981230987879927244284909188
-84580156166097919133875499200524063689912560717606
-05886116467109405077541002256983155200055935729725
-71636269561882670428252483600823257530420752963450
+    73167176531330624919225119674426574742355349194934
+    96983520312774506326239578318016984801869478851843
+    85861560789112949495459501737958331952853208805511
+    12540698747158523863050715693290963295227443043557
+    66896648950445244523161731856403098711121722383113
+    62229893423380308135336276614282806444486645238749
+    30358907296290491560440772390713810515859307960866
+    70172427121883998797908792274921901699720888093776
+    65727333001053367881220235421809751254540594752243
+    52584907711670556013604839586446706324415722155397
+    53697817977846174064955149290862569321978468622482
+    83972241375657056057490261407972968652414535100474
+    82166370484403199890008895243450658541227588666881
+    16427171479924442928230863465674813919123162824586
+    17866458359124566529476545682848912883142607690042
+    24219022671055626321111109370544217506941658960408
+    07198403850962455444362981230987879927244284909188
+    84580156166097919133875499200524063689912560717606
+    05886116467109405077541002256983155200055935729725
+    71636269561882670428252483600823257530420752963450
 
 Find the thirteen adjacent digits in the 1000-digit number that have the
 greatest product. What is the value of this product?
@@ -53,13 +55,15 @@ N = """73167176531330624919225119674426574742355349194934\
 
 
 def str_eval(s: str) -> int:
-    """Returns product of digits in given string n
+    """
+    Returns product of digits in given string n
 
     >>> str_eval("987654321")
     362880
     >>> str_eval("22222222")
     256
     """
+
     product = 1
     for digit in s:
         product *= int(digit)
@@ -67,12 +71,11 @@ def str_eval(s: str) -> int:
 
 
 def solution(n: str = N) -> int:
-    """Find the thirteen adjacent digits in the 1000-digit number n that have
+    """
+    Find the thirteen adjacent digits in the 1000-digit number n that have
     the greatest product and returns it.
-
-    >>> solution(N)
-    23514624000
     """
+
     largest_product = -sys.maxsize - 1
     substr = n[:13]
     cur_index = 13
@@ -88,4 +91,4 @@ def solution(n: str = N) -> int:
 
 
 if __name__ == "__main__":
-    print(solution(N))
+    print(f"{solution() = }")

project_euler/problem_009/sol1.py

 """
-Problem 9: https://projecteuler.net/problem=9
+Project Euler Problem 9: https://projecteuler.net/problem=9
+
+Special Pythagorean triplet
 
 A Pythagorean triplet is a set of three natural numbers, a < b < c, for which,
+
     a^2 + b^2 = c^2
+
 For example, 3^2 + 4^2 = 9 + 16 = 25 = 5^2.
 
 There exists exactly one Pythagorean triplet for which a + b + c = 1000.
-Find the product abc.
+Find the product a*b*c.
+
+References:
+    - https://en.wikipedia.org/wiki/Pythagorean_triple
 """
 
 
 def solution() -> int:
     """
-     Returns the product of a,b,c which are Pythagorean Triplet that satisfies
-     the following:
-     1. a < b < c
-     2. a**2 + b**2 = c**2
-     3. a + b + c = 1000
+    Returns the product of a,b,c which are Pythagorean Triplet that satisfies
+    the following:
+      1. a < b < c
+      2. a**2 + b**2 = c**2
+      3. a + b + c = 1000
+
     # The code below has been commented due to slow execution affecting Travis.
     # >>> solution()
     # 31875000
     """
+
     for a in range(300):
         for b in range(400):
             for c in range(500):
@@ -32,16 +41,17 @@ def solution() -> int:
 
 def solution_fast() -> int:
     """
-     Returns the product of a,b,c which are Pythagorean Triplet that satisfies
-     the following:
-     1. a < b < c
-     2. a**2 + b**2 = c**2
-     3. a + b + c = 1000
+    Returns the product of a,b,c which are Pythagorean Triplet that satisfies
+    the following:
+      1. a < b < c
+      2. a**2 + b**2 = c**2
+      3. a + b + c = 1000
 
     # The code below has been commented due to slow execution affecting Travis.
     # >>> solution_fast()
     # 31875000
     """
+
     for a in range(300):
         for b in range(400):
             c = 1000 - a - b
@@ -66,4 +76,4 @@ def benchmark() -> None:
 
 
 if __name__ == "__main__":
-    benchmark()
+    print(f"{solution() = }")

project_euler/problem_009/sol2.py

 """
-Problem 9: https://projecteuler.net/problem=9
+Project Euler Problem 9: https://projecteuler.net/problem=9
+
+Special Pythagorean triplet
 
 A Pythagorean triplet is a set of three natural numbers, a < b < c, for which,
+
     a^2 + b^2 = c^2
+
 For example, 3^2 + 4^2 = 9 + 16 = 25 = 5^2.
 
 There exists exactly one Pythagorean triplet for which a + b + c = 1000.
-Find the product abc.
+Find the product a*b*c.
+
+References:
+    - https://en.wikipedia.org/wiki/Pythagorean_triple
 """
 
 
 def solution(n: int = 1000) -> int:
     """
-     Return the product of a,b,c which are Pythagorean Triplet that satisfies
-     the following:
-     1. a < b < c
-     2. a**2 + b**2 = c**2
-     3. a + b + c = n
-
-    >>> solution(1000)
-    31875000
+    Return the product of a,b,c which are Pythagorean Triplet that satisfies
+    the following:
+      1. a < b < c
+      2. a**2 + b**2 = c**2
+      3. a + b + c = n
+
+    >>> solution(36)
+    1620
+    >>> solution(126)
+    66780
     """
+
     product = -1
     candidate = 0
     for a in range(1, n // 3):
-        """Solving the two equations a**2+b**2=c**2 and a+b+c=N eliminating c"""
+        # Solving the two equations a**2+b**2=c**2 and a+b+c=N eliminating c
         b = (n * n - 2 * a * n) // (2 * n - 2 * a)
         c = n - a - b
         if c * c == (a * a + b * b):
@@ -35,4 +45,4 @@ def solution(n: int = 1000) -> int:
 
 
 if __name__ == "__main__":
-    print(solution(int(input().strip())))
+    print(f"{solution() = }")

project_euler/problem_009/sol3.py

 """
-Problem 9: https://projecteuler.net/problem=9
+Project Euler Problem 9: https://projecteuler.net/problem=9
+
+Special Pythagorean triplet
 
 A Pythagorean triplet is a set of three natural numbers, a < b < c, for which,
 
@@ -8,22 +10,25 @@ A Pythagorean triplet is a set of three natural numbers, a < b < c, for which,
 For example, 3^2 + 4^2 = 9 + 16 = 25 = 5^2.
 
 There exists exactly one Pythagorean triplet for which a + b + c = 1000.
-Find the product abc.
+Find the product a*b*c.
+
+References:
+    - https://en.wikipedia.org/wiki/Pythagorean_triple
 """
 
 
 def solution() -> int:
     """
-     Returns the product of a,b,c which are Pythagorean Triplet that satisfies
-     the following:
-
-     1. a**2 + b**2 = c**2
-     2. a + b + c = 1000
+    Returns the product of a,b,c which are Pythagorean Triplet that satisfies
+    the following:
+      1. a**2 + b**2 = c**2
+      2. a + b + c = 1000
 
     # The code below has been commented due to slow execution affecting Travis.
     # >>> solution()
     # 31875000
     """
+
     return [
         a * b * (1000 - a - b)
         for a in range(1, 999)
@@ -33,4 +38,4 @@ def solution() -> int:
 
 
 if __name__ == "__main__":
-    print(solution())
+    print(f"{solution() = }")

project_euler/problem_010/sol1.py

 """
-https://projecteuler.net/problem=10
+Project Euler Problem 10: https://projecteuler.net/problem=10
+
+Summation of primes
 
-Problem Statement:
 The sum of the primes below 10 is 2 + 3 + 5 + 7 = 17.
 
 Find the sum of all the primes below two million.
+
+References:
+    - https://en.wikipedia.org/wiki/Prime_number
 """
+
 from math import sqrt
 
 
 def is_prime(n: int) -> bool:
-    """Returns boolean representing primality of given number num.
+    """
+    Returns boolean representing primality of given number num.
+
     >>> is_prime(2)
     True
     >>> is_prime(3)
@@ -20,6 +27,7 @@ def is_prime(n: int) -> bool:
     >>> is_prime(2999)
     True
     """
+
     for i in range(2, int(sqrt(n)) + 1):
         if n % i == 0:
             return False
@@ -28,11 +36,9 @@ def is_prime(n: int) -> bool:
 
 
 def solution(n: int = 2000000) -> int:
-    """Returns the sum of all the primes below n.
+    """
+    Returns the sum of all the primes below n.
 
-    # The code below has been commented due to slow execution affecting Travis.
-    # >>> solution(2000000)
-    # 142913828922
     >>> solution(1000)
     76127
     >>> solution(5000)
@@ -42,6 +48,7 @@ def solution(n: int = 2000000) -> int:
     >>> solution(7)
     10
     """
+
     if n > 2:
         sum_of_primes = 2
     else:
@@ -55,4 +62,4 @@ def solution(n: int = 2000000) -> int:
 
 
 if __name__ == "__main__":
-    print(solution(int(input().strip())))
+    print(f"{solution() = }")

project_euler/problem_010/sol2.py

 """
-https://projecteuler.net/problem=10
+Project Euler Problem 10: https://projecteuler.net/problem=10
+
+Summation of primes
 
-Problem Statement:
 The sum of the primes below 10 is 2 + 3 + 5 + 7 = 17.
 
 Find the sum of all the primes below two million.
+
+References:
+    - https://en.wikipedia.org/wiki/Prime_number
 """
 import math
 from itertools import takewhile
@@ -12,7 +16,9 @@ from typing import Iterator
 
 
 def is_prime(number: int) -> bool:
-    """Returns boolean representing primality of given number num.
+    """
+    Returns boolean representing primality of given number num.
+
     >>> is_prime(2)
     True
     >>> is_prime(3)
@@ -22,12 +28,17 @@ def is_prime(number: int) -> bool:
     >>> is_prime(2999)
     True
     """
+
     if number % 2 == 0 and number > 2:
         return False
     return all(number % i for i in range(3, int(math.sqrt(number)) + 1, 2))
 
 
 def prime_generator() -> Iterator[int]:
+    """
+    Generate a list sequence of prime numbers
+    """
+
     num = 2
     while True:
         if is_prime(num):
@@ -36,11 +47,9 @@ def prime_generator() -> Iterator[int]:
 
 
 def solution(n: int = 2000000) -> int:
-    """Returns the sum of all the primes below n.
+    """
+    Returns the sum of all the primes below n.
 
-    # The code below has been commented due to slow execution affecting Travis.
-    # >>> solution(2000000)
-    # 142913828922
     >>> solution(1000)
     76127
     >>> solution(5000)
@@ -50,8 +59,9 @@ def solution(n: int = 2000000) -> int:
     >>> solution(7)
     10
     """
+
     return sum(takewhile(lambda x: x < n, prime_generator()))
 
 
 if __name__ == "__main__":
-    print(solution(int(input().strip())))
+    print(f"{solution() = }")

project_euler/problem_010/sol3.py

 """
-https://projecteuler.net/problem=10
+Project Euler Problem 10: https://projecteuler.net/problem=10
+
+Summation of primes
 
-Problem Statement:
 The sum of the primes below 10 is 2 + 3 + 5 + 7 = 17.
 
 Find the sum of all the primes below two million.
+
+References:
+    - https://en.wikipedia.org/wiki/Prime_number
+    - https://en.wikipedia.org/wiki/Sieve_of_Eratosthenes
 """
 
 
 def solution(n: int = 2000000) -> int:
-    """Returns the sum of all the primes below n using Sieve of Eratosthenes:
+    """
+    Returns the sum of all the primes below n using Sieve of Eratosthenes:
 
-    https://en.wikipedia.org/wiki/Sieve_of_Eratosthenes
     The sieve of Eratosthenes is one of the most efficient ways to find all primes
     smaller than n when n is smaller than 10 million.  Only for positive numbers.
 
-    >>> solution(2_000_000)
-    142913828922
-    >>> solution(1_000)
+    >>> solution(1000)
     76127
-    >>> solution(5_000)
+    >>> solution(5000)
     1548136
-    >>> solution(10_000)
+    >>> solution(10000)
     5736396
     >>> solution(7)
     10
-    >>> solution(7.1)  # doctest: +ELLIPSIS
+    >>> solution(7.1)  # doctest: +ELLIPSIS
     Traceback (most recent call last):
     ...
     TypeError: 'float' object cannot be interpreted as an integer
-    >>> solution(-7)  # doctest: +ELLIPSIS
+    >>> solution(-7)  # doctest: +ELLIPSIS
     Traceback (most recent call last):
     ...
     IndexError: list assignment index out of range
-    >>> solution("seven")  # doctest: +ELLIPSIS
+    >>> solution("seven")  # doctest: +ELLIPSIS
     Traceback (most recent call last):
     ...
     TypeError: can only concatenate str (not "int") to str
     """
+
     primality_list = [0 for i in range(n + 1)]
     primality_list[0] = 1
     primality_list[1] = 1
@@ -54,4 +58,4 @@ def solution(n: int = 2000000) -> int:
 
 
 if __name__ == "__main__":
-    print(solution(int(input().strip())))
+    print(f"{solution() = }")