  We pose the following new variant of the Kuratowski closure-complement
problem: How many distinct sets may be obtained by starting with a set $A$ of a
Polish space $X$, and applying only closure, complementation, and the $d$
operator, as often as desired, in any order? The set operator $d$ was studied
by Kuratowski in his foundational text \textit{Topology: Volume I}; it assigns
to $A$ the collection $dA$ of all points of second category for $A$. We show
that in ZFC set theory, the answer to this variant problem is $22$. In a
distinct system equiconsistent with ZFC, namely ZF+DC+PB, the answer is only
$18$.
