A solution is obviously correct if it gives an x, y, and z of the peak such that when you use any of the four measured heights to find the slope, that slope finishes the equation:

(x-x')^2+(y-y')^2=m^2(z-z')^2
(or maybe it's 1/m^2 instead of m^2 -- irrelavent details)

and the other three measurements all fit into that equation with the given x, y, z, and m.

So, when given a solution, it will be clear that it is a solution. Is it clear that there's only one solution for the non-degenerate case? Not yet. But the goal is the same as for the colored points last week that we wanted to separate with (n-1)-dimensional hyperplanes -- can A solution (or even ALL solutions) be found? How?