def prob12(limit=500):
    """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?
    """
    tri = 0     # triangle number
    add = 0
    divs = 0
    while divs <= limit:
        #print
        divs = 0
        add += 1
        tri += add
        # each divisor below rt has one above
        for i in range(1, int(tri ** 0.5) + 1):
            if tri % i == 0:
                divs += 2
        if tri == (int(tri ** 0.5) ** 2):   # if perfect square only one divisor
            divs -= 1                   # so correct
        #print 'divs', divs
        #print tri
    return tri