Okay, so this problem is really kicking my butt (read: ~6 hours). We're given four values and there are only TWO degrees of freedom, so the problem is overspecified and should be easy to solve (darned non-linearities). Why do I say there are only two degrees of freedom? If you're given the slope and height, its easy to compute (based on the heights measured) how far each corner of the grid is horizontally from the peak. From that, it's not hard to get the x,y coordinates of the peak. And given the x,y coordinates, it's easy to get the height of the peak and its slope. So there's definitely only two degrees of freedom.
Yet the solution continues to elude me!!!
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