I thought of a kino solution to part 3 that Im too lazy to write myself. Imagine ISO2-xyzw ijkl = n. We do i*x^3 + j*y^2... = 137, express i as a function of j k l, so we can find if the room to minimize it is sufficient. If it is we search for a way to minimize it and if we find it vote invalid if not (in either of the two), we consider i fixed, so we express everything in terms of j instead and so on, till the second to last var, at which point we can validate the vote