12.py

# The sequence of triangle numbers is generated by adding the natural numbers.
# So the 7th triangle number would be 1 + 2 + 3 + 4 + 5 + 6 + 7 = 28.
# The first ten terms would be:

# 1, 3, 6, 10, 15, 21, 28, 36, 45, 55, ...

# Let us list the factors of the first seven triangle numbers:

#  1: 1
#  3: 1,3
#  6: 1,2,3,6
# 10: 1,2,5,10
# 15: 1,3,5,15
# 21: 1,3,7,21
# 28: 1,2,4,7,14,28
# We can see that 28 is the first triangle number to have over five divisors.

# What is the value of the first triangle number to have over
# five hundred divisors?

from math import sqrt
import time

t1 = time.time()

s = 0
for i in range(100000):
    s += i
    factors = 2  # 1, i
    for j in range(1, int(sqrt(s)) + 1):
        if(s % j == 0):
            factors += 2  # factor, s/factor
    if(factors > 500):
        print factors, s, i
        break

print time.time() - t1