MathDB

Distinct planes

p_1,p_2,....,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 minimum possible values of

k

<span class='latex-bold'>(A)</span>\ 8\qquad<span class='latex-bold'>(B)</span>\ 12\qquad<span class='latex-bold'>(C)</span>\ 20\qquad<span class='latex-bold'>(D)</span>\ 23\qquad<span class='latex-bold'>(E)</span>\ 24

Problem Statement