  We consider the covering of a ball in certain normed spaces by its congruent
subsets and show that if the finite number of sets is not greater than the
dimensionality of the space, then the centre of the ball either belongs to the
interior of each set, or doesn't belong to the interior of any set. We also
provide some examples when it belongs to the interior of exactly one set. These
are the specific cases of the modified problem originally posed for dissection.
