answer:When you say that there will be 42 points if the x y z are unique, did you mean 48? There are six ways to arrange the numbers and eight combinations of the signs. Besides that, one other observation might be determining not the possible radii, but the different possible values for the number of points intersected. Will it always be a multiple of two (I think so)? What conditions cause it to be a multiple of four or eight? With this info, we can reverse- engineer the answer. For the question of >95, it becomes the sphere with at least 96, which is a multiple of eight. If we could find a pattern as to which radii cause multiples of eight, we could limit the number of solutions.