"""
 problem 9 from projecteuler.net, done in class Oct 11 2011

 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.

"""

for a in range(1, 333):       # a,b,c sum to 1000 and a is smallest
    for b in range(a+1, 667):
        c = 1000 - a - b
        if a**2 + b**2 == c**2:
            print (a, b, c)
            print a*b*c