Solution to problem 45

src/Python/Problem045.py

@@ -0,0 +1,42 @@
+#!/usr/bin/env python3
+"""
+Created on 09 Sep 2021
+
+@author: David Doblas Jiménez
+@email: daviddoji@pm.me
+
+Solution for problem 45 of Project Euler
+https://projecteuler.net/problem=45
+"""
+
+from utils import timeit
+
+def pentagonal(n):
+    return int(n*(3*n-1)/2)
+
+def hexagonal(n):
+    return int(n*(2*n-1))
+
+@timeit("Problem 45")
+def compute():
+    """
+    Triangle, pentagonal, and hexagonal numbers are generated by the following formulae:
+        Triangle 	  	Tn=n(n+1)/2 	  	1, 3, 6, 10, 15, ...
+        Pentagonal 	  	Pn=n(3n−1)/2 	  	1, 5, 12, 22, 35, ...
+        Hexagonal 	  	Hn=n(2n−1) 	  	    1, 6, 15, 28, 45, ...
+
+    It can be verified that T285 = P165 = H143 = 40755.
+
+    Find the next triangle number that is also pentagonal and hexagonal.
+    """
+    pentagonal_list = set(pentagonal(n) for n in range(2,100_000))
+    # all hexagonal numbers are also triangle numbers!
+    hexagonal_list = set(hexagonal(n) for n in range(2,100_000))
+
+    ans = sorted(hexagonal_list & pentagonal_list)
+    # First one is already known
+    return ans[1]
+
+if __name__ == "__main__":
+
+    print(f"Result for Problem 45: {compute()}")