Permutations + brute force

#http://stackoverflow.com/questions/10388060/solving-puzzle-in-python
import itertools as it

weight = 40
full = range(1,41)
comb = [x for x in it.combinations(full,4) if sum(x)==40]

for perm in comb:
    list = []
    list.append(perm[0] + perm[1] + perm[2] + perm[3])
    list.append(perm[0] + perm[1] + perm[2] - perm[3])
    list.append(perm[0] + perm[1] - perm[2] + perm[3])
    list.append(perm[0] + perm[1] - perm[2] - perm[3])
    list.append(perm[0] - perm[1] + perm[2] + perm[3])
    list.append(perm[0] - perm[1] + perm[2] - perm[3])
    list.append(perm[0] - perm[1] - perm[2] + perm[3])
    list.append(perm[0] - perm[1] - perm[2] - perm[3])
    list.append(- perm[0] + perm[1] + perm[2] + perm[3])
    list.append(- perm[0] + perm[1] + perm[2] - perm[3])
    list.append(- perm[0] + perm[1] - perm[2] + perm[3])
    list.append(- perm[0] + perm[1] - perm[2] - perm[3])
    list.append(- perm[0] - perm[1] + perm[2] + perm[3])
    list.append(- perm[0] - perm[1] + perm[2] - perm[3])
    list.append(- perm[0] - perm[1] - perm[2] + perm[3])
    list.append(- perm[0] - perm[1] - perm[2] - perm[3])
    #take out 3s
    list.append(perm[0] + perm[1] + perm[2])
    list.append(perm[0] + perm[1] - perm[2])
    list.append(perm[0] - perm[1] + perm[2])
    list.append(perm[0] - perm[1] - perm[2])
    list.append(- perm[0] + perm[1] + perm[2])
    list.append(- perm[0] + perm[1] - perm[2])
    list.append(- perm[0] - perm[1] + perm[2])
    list.append(- perm[0] - perm[1] - perm[2])
    # take out 2s
    list.append(perm[0] + perm[1] + perm[3])
    list.append(perm[0] + perm[1] - perm[3])
    list.append(perm[0] - perm[1] + perm[3])
    list.append(perm[0] - perm[1] - perm[3])
    list.append(- perm[0] + perm[1] + perm[3])
    list.append(- perm[0] + perm[1] - perm[3])
    list.append(- perm[0] - perm[1] + perm[3])
    list.append(- perm[0] - perm[1] - perm[3])
    # take out 1s
    list.append(perm[0] + perm[2] + perm[3])
    list.append(perm[0] + perm[2] - perm[3])
    list.append(perm[0] - perm[2] + perm[3])
    list.append(perm[0] - perm[2] - perm[3])
    list.append(- perm[0] + perm[2] + perm[3])
    list.append(- perm[0] + perm[2] - perm[3])
    list.append(- perm[0] - perm[2] + perm[3])
    list.append(- perm[0] - perm[2] - perm[3])
    # take out 0s
    list.append(perm[1] + perm[2] + perm[3])
    list.append(perm[1] + perm[2] - perm[3])
    list.append(perm[1] - perm[2] + perm[3])
    list.append(perm[1] - perm[2] - perm[3])
    list.append(- perm[1] + perm[2] + perm[3])
    list.append(- perm[1] + perm[2] - perm[3])
    list.append(- perm[1] - perm[2] + perm[3])
    list.append(- perm[1] - perm[2] - perm[3])
    # take out 3, 2
    list.append(perm[0] + perm[1])
    list.append(perm[0] - perm[1])
    list.append(- perm[0] + perm[1])
    list.append(- perm[0] - perm[1])
    # take out 3, 1
    list.append(perm[0] + perm[2])
    list.append(perm[0] - perm[2])
    list.append(- perm[0] + perm[2])
    list.append(- perm[0] - perm[2])
    # take out 3, 0
    list.append(perm[1] + perm[2])
    list.append(perm[1] - perm[2])
    list.append(- perm[1] + perm[2])
    list.append(- perm[1] - perm[2])
    # take out 2, 1
    list.append(perm[0] + perm[3])
    list.append(perm[0] - perm[3])
    list.append(- perm[0] + perm[3])
    list.append(- perm[0] - perm[3])
    # take out 2, 0
    list.append(perm[1] + perm[3])
    list.append(perm[1] - perm[3])
    list.append(- perm[1] + perm[3])
    list.append(- perm[1] - perm[3])
    list.append(perm[1] + perm[3])
    list.append(perm[1] - perm[3])
    list.append(- perm[1] + perm[3])
    list.append(- perm[1] - perm[3])
    # take out 1, 0
    list.append(perm[2] + perm[3])
    list.append(perm[2] - perm[3])
    list.append(- perm[2] + perm[3])
    list.append(- perm[2] - perm[3])
    # only 0 or 1 or 2, or 3
    list.append(perm[0])
    list.append(perm[1])
    list.append(perm[2])
    list.append(perm[3])

    list_good = True
    for x in range(1, 41):
        if x not in list:
            list_good = False
    if list_good:
        print list, perm