def prob9(total=1000):
    """
    A Pythagorean triplet is a set of three natural numbers, a < b < c, for
    which, a**2 + b**2 = c**2

    For example, 3**2 + 4**2 = 9 + 16 = 25 = 5**2.

    There exists exactly one Pythagorean triplet for which a + b + c = 1000.
    Find the product abc.
    """
    a = 1

    while True:
        for i in range(2, total):
            b = i
            c = total - a - b
            if a ** 2 + b ** 2 == c ** 2:
                return a * b * c
        a += 1