Solution to ProjectEuler 231

project_euler/problem_231/sol1.py

@@ -0,0 +1,39 @@
+"""
+Project Euler Problem 231: https://projecteuler.net/problem=231
+
+The binomial coefficient choose(10, 3)=120.
+120 = 2^3 * 3 * 5 = 2 * 2 * 2 * 3 * 5, and 2 + 2 + 2 + 3 + 5 = 14.
+So the sum of the terms in the prime factorisation of choose(10, 3) is 14.
+
+Find the sum of the terms in the prime factorisation of choose(20_000_000, 15_000_000).
+"""
+
+from sympy import factorint
+from collections import Counter
+
+
+def solution(n: int = 20_000_000, k: int = 15_000_000) -> int:
+    """
+    Returns the sum of all the multiples of 3 or 5 below n.
+
+    >>> solution(10, 3)
+    14
+    """
+
+    a, b = 20_000_000, 15_000_000
+    top, bot = [], []
+    for t in range(b + 1, a + 1):
+        top.extend(factorint(t, multiple=True))
+    for b in range(1, a - b + 1):
+        bot.extend(factorint(b, multiple=True))
+
+    top = Counter(top)
+    bot = Counter(bot)
+    s = 0
+    for k, v in top.items():
+        s += k * (v - bot[k])
+    return s
+
+
+if __name__ == "__main__":
+    print(f"{solution() = }")