Problem 12 brings back an interesting mathematical concept: triangular numbers. Triangular numbers (and the formula for finding one) are the slightly more sophisticated approach
I mentioned in my writeup for Problem 6. Writing a generator for triangular numbers is easy enough, as is writing some logic to factorize (not prime factorize) a number. Given those two, the solution is easy enough.
"""Solves Problem 12 of Project Euler."""
import math
def factors(to_factor):
"""Find the factors of to_factor."""
factors = []
divisor = 1
while (divisor <= int(math.sqrt(to_factor))):
if not to_factor % divisor:
quotient = to_factor / divisor
factors.append(divisor)
factors.append(quotient)
divisor += 1
return factors
def triangular_numbers():
"""Generate the triangular numbers."""
current = 0
position = 1
while True:
current += position
position += 1
yield current
def problem_12(min_divisors):
"""Finds the first triangular number to have more than 500 divisors."""
for triangular in triangular_numbers():
cur_factors = factors(triangular)
if len(cur_factors) > min_divisors:
return triangular
if __name__ == '__main__':
print problem_12(500)
Back to flipping out...
