Broken Weight problem

weights.py

# Response to challenge at http://beust.com/weblog/2011/10/30/a-new-coding-challenge/
# Further (braintwistingly) compact version of the same logic : https://gist.github.com/1326654
import itertools
n = 40
weights = tuple((w1,w2,w3,n-(w1+w2+w3)) for w1 in range(1,n) for w2 in range(w1,n - w1) for w3 in range(w2, n-w1-w2) if n-(w1+w2+w3) -w3 >= 0)
for weight in weights :
    allvals = list(val for val in range(1,n + 1))
    for clength in range(1,5) :
        for combo in itertools.combinations(weight,clength) :
            other = list(weight)
            for c in combo :
                other.remove(c)
            for olength in range(len(other) + 1) :
                for o in itertools.combinations(other,olength) :
                    diff = abs(sum(combo) - sum(o))
                    if diff in allvals : allvals.remove(diff)
    if len(allvals) == 0 : print weight