  Lindsay and Basak (2000) posed the question of how far from normality could a
distribution be if it matches $k$ normal moments. They provided a bound on the
maximal difference in c.d.f.'s, and implied that these bounds were attained. It
will be shown here that in fact the bound is not attained if the number of even
moments matched is odd. An explicit solution is developed as a symmetric
distribution with a finite number of mass points when the number of even
moments matched is even, and this bound for the even case is shown to hold as
an explicit limit for the subsequent odd case.
