gistfile1.py

import itertools
for a, b, c, d, e, f in itertools.product(range(1, 10), range(1, 10), range(1, 10), range(1, 10), range(1, 10), range(1, 10)):
    if (a + b + c == 18 and
        d + e + f == 18 and
        a + d == b + e and
        b + e == c + f and
        int(str(e) + str(f)) in [16, 25, 36, 49, 64, 81] and
        len(set([a, b, c, d, e, f])) == 6):
        print a, b, c, d, e, f