Python Implementation of Problem 45

View source code here on GitHub!

Includes

  • math.hexagonal()

  • math.pentagonal()

  • math.triangle()

Problem Solution

Project Euler Problem 45

Problem:

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.

python.src.p0045.main() → int
 1"""
 2Project Euler Problem 45
 3
 4Problem:
 5
 6Triangle, pentagonal, and hexagonal numbers are generated by the following formulae:
 7Triangle 	  	Tn=n(n+1)/2 	  	1, 3, 6, 10, 15, ...
 8Pentagonal 	  	Pn=n(3n−1)/2 	  	1, 5, 12, 22, 35, ...
 9Hexagonal 	  	Hn=n(2n−1) 	      	1, 6, 15, 28, 45, ...
10
11It can be verified that T285 = P165 = H143 = 40755.
12
13Find the next triangle number that is also pentagonal and hexagonal.
14"""
15from .lib.math import hexagonal, pentagonal, triangle
16
17
18def main() -> int:
19    T_idx = 286
20    P_idx = 166
21    H_idx = 144
22    T_val = triangle(T_idx)
23    P_val = pentagonal(P_idx)
24    H_val = hexagonal(H_idx)
25    while not (T_val == P_val == H_val):
26        # print(P_val, T_val, H_val)
27        while T_val < P_val or T_val < H_val:
28            T_idx += 1
29            T_val = triangle(T_idx)
30        while P_val < T_val or P_val < H_val:
31            P_idx += 1
32            P_val = pentagonal(P_idx)
33        while H_val < P_val or H_val < T_val:
34            H_idx += 1
35            H_val = hexagonal(H_idx)
36    return T_val

Tags: figurate-number, triangle-number