{"status": "success", "data": {"description_md": "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 $k$?\n\n$\\textbf{(A)}\\ 8\\qquad\\textbf{(B)}\\ 12\\qquad\\textbf{(C)}\\ 20\\qquad\\textbf{(D)}\\ 23\\qquad\\textbf{(E)}\\ 24$\n___\nFull credit goes to [MAA](https://maa.org/) for authoring these problems. These problems were taken on the [AOPS](https://artofproblemsolving.com/) website.", "description_html": "<p>Distinct planes  <span class=\"katex--inline\">p_1,p_2,....,p_k</span>  intersect the interior of a cube  <span class=\"katex--inline\">Q</span> . Let  <span class=\"katex--inline\">S</span>  be the union of the faces of  <span class=\"katex--inline\">Q</span>  and let  <span class=\"katex--inline\">P =\\bigcup_{j=1}^{k}p_{j}</span> . The intersection of  <span class=\"katex--inline\">P</span>  and  <span class=\"katex--inline\">S</span>  consists of the union of all segments joining the midpoints of every pair of edges belonging to the same face of  <span class=\"katex--inline\">Q</span> . What is the difference between the maximum and minimum possible values of  <span class=\"katex--inline\">k</span> ?</p>&#10;<p> <span class=\"katex--inline\">\\textbf{(A)}\\ 8\\qquad\\textbf{(B)}\\ 12\\qquad\\textbf{(C)}\\ 20\\qquad\\textbf{(D)}\\ 23\\qquad\\textbf{(E)}\\ 24</span> </p>&#10;<hr><p>Full credit goes to <a href=\"https://maa.org/\">MAA</a> for authoring these problems. These problems were taken on the <a href=\"https://artofproblemsolving.com/\">AOPS</a> website.</p>", "hints_md": "", "hints_html": "", "editorial_md": "", "editorial_html": "", "flag_hint": "", "point_value": 5, "problem_name": "2012 AMC 12A Problem 22", "can_next": true, "can_prev": true, "nxt": "/problem/12_amc12A_p23", "prev": "/problem/12_amc12A_p21"}}