{"status": "success", "data": {"description_md": "The number $2013$ is expressed in the form $$2013=\\frac{a_1!a_2!\\cdots a_m!}{b_1!b_2!\\cdots b_n!},$$ where $a_1\\ge a_2\\ge\\cdots\\ge a_m$ and $b_1\\ge b_2\\ge\\cdots\\ge b_n$ are positive integers and $a_1+b_1$ is as small as possible. What is $|a_1-b_1|$?\n\n$\\textbf{(A)}\\ 1\\qquad\\textbf{(B)}\\ 2\\qquad\\textbf{(C)}\\ 3\\qquad\\textbf{(D)}\\ 4\\qquad\\textbf{(E)}\\ 5$", "description_html": "<p>The number  <span class=\"katex--inline\">2013</span>  is expressed in the form  <span class=\"katex--display\">2013=\\frac{a_1!a_2!\\cdots a_m!}{b_1!b_2!\\cdots b_n!},</span>  where  <span class=\"katex--inline\">a_1\\ge a_2\\ge\\cdots\\ge a_m</span>  and  <span class=\"katex--inline\">b_1\\ge b_2\\ge\\cdots\\ge b_n</span>  are positive integers and  <span class=\"katex--inline\">a_1+b_1</span>  is as small as possible. What is  <span class=\"katex--inline\">|a_1-b_1|</span> ?</p>\n<p> <span class=\"katex--inline\">\\textbf{(A)}\\ 1\\qquad\\textbf{(B)}\\ 2\\qquad\\textbf{(C)}\\ 3\\qquad\\textbf{(D)}\\ 4\\qquad\\textbf{(E)}\\ 5</span> </p>\n<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": 3, "problem_name": "2013 AMC 10B Problem 20", "can_next": true, "can_prev": true, "nxt": "/problem/13_amc10B_p21", "prev": "/problem/13_amc10B_p19"}}