Project Euler problem148

project_euler/problem_148/sol1.py

@@ -0,0 +1,52 @@
+"""
+Project Euler Problem 148 : https://projecteuler.net/problem=148
+Author:	Sai Teja Manchi
+Problem Statement:
+We can easily verify that none of the entries in the
+first seven rows of Pascal's triangle are divisible by 7:
+                               1
+                          1          1
+                     1          2          1
+                1          3          3          1
+           1          4          6          4          1
+      1          5         10         10          5          1
+1          6         15         20         15          6          1
+However, if we check the first one hundred rows, we will find that
+only 2361 of the 5050 entries are not divisible by 7.
+Find the number of entries which are not divisible by 7
+in the first one billion (109) rows of Pascal's triangle.
+"""
+
+
+def get_num_binomials(row_num: int) -> int:
+    """
+    To compute the number of entries in the nth row of
+    pascal triangle that are not divisble by 7.
+    To compute the number of entries in the nth row of
+    pascal triangle that are not divisble by 7.
+    Based on Lucas Theroem it is the product of (each digit in the base 7 n + 1)
+    Reference: https://brilliant.org/wiki/lucas-theorem/
+    """
+    cnt = 1
+    while row_num > 0:
+        cnt *= (row_num % 7) + 1
+        row_num //= 7
+    return cnt
+
+
+def solution(pascal_row_count: int = 10**9) -> int:
+    """
+    To evaluate the solution, use solution()
+    >>> solution(3)
+    6
+    >>> solution(10)
+    40
+    >>> solution(100)
+    2361
+    """
+
+    result = 0
+    for i in range(pascal_row_count):
+        result += get_num_binomials(i)
+
+    return result