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 SonOfLilit / choose
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def words(x):
    result = []
    i = 0
    while x:
        if x & 1:
            result.append(i)
        x >>= 1
        i += 1
    return result
 
def popcnt(x):
    count = 0
    while x:
        count += x & 1
        x >>= 1
    return count
 
six_of_sixteen = [words(x) for x in range(1<<16) if popcnt(x) == 6]
assert len(six_of_sixteen) == 8008
for code in six_of_sixteen:
    errors = set(range(1, 16))
    for i, a in enumerate(code):
        for b in code[i+1:]:
            if a ^ b in errors:
                errors.remove(a ^ b)
    if not errors:
        print "good"
        break

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