Our professor hinted that the brute force way of solving this is naive and that there is a simpler way, the problem is I don't see it. My idea was to set this into a matrix with 3 equations and 3 unknowns and try to solve x, y, and z. This approach started to become very messy and I would get an answer like . So my question is really this, is there anybody out there that sees the trick for this problem that could give me a pointer. thanks in advance!