  Given a finite set of points $\Gamma$ in $\mathbb P^{k-1}$ not all contained
in a hyperplane, the "fitting problem" asks what is the maximum number
$hyp(\Gamma)$ of these points that can fit in some hyperplane and what is (are)
the equation(s) of such hyperplane(s). If $\Gamma$ has the property that any
$k-1$ of its points span a hyperplane, then $hyp(\Gamma)=nil(I)+k-2$, where
$nil(I)$ is the index of nilpotency of an ideal constructed from the
homogeneous coordinates of the points of $\Gamma$. Note that in $\mathbb P^2$
any two points span a line, and we find that the maximum number of collinear
points of any given set of points $\Gamma\subset\mathbb P^2$ equals the index
of nilpotency of the corresponding ideal, plus one.
