Question 22
Distinct planes $p_1,$ $p_2,$ $\ldots,$ $p_k$ intersect the interior of a cube $Q.$ Let $S$ be the union of the faces of $Q$ and let $P = \bigcup_{j=1}^{k} p_j.$ The intersection of $P$ and $S$ consists of the union of all segments joining the midpoints of every pair of edges belonging to the same face of $Q.$ What is the difference between the maximum and the minimum possible values of $k?$