{"status": "success", "data": {"description_md": "For $k > 0$, let $I_k = 10\\ldots 064$, where there are $k$ zeros between the $1$ and the $6$.  Let $N(k)$ be the number of factors of $2$ in the prime factorization of $I_k$.  What is the maximum value of $N(k)$?\n\n$\\mathrm{(A)}\\ 6\n\\qquad\n\\mathrm{(B)}\\ 7\n\\qquad\n\\mathrm{(C)}\\ 8\n\\qquad\n\\mathrm{(D)}\\ 9\n\\qquad\n\\mathrm{(E)}\\ 10$", "description_html": "<p>For  <span class=\"katex--inline\">k &gt; 0</span> , let  <span class=\"katex--inline\">I_k = 10\\ldots 064</span> , where there are  <span class=\"katex--inline\">k</span>  zeros between the  <span class=\"katex--inline\">1</span>  and the  <span class=\"katex--inline\">6</span> .  Let  <span class=\"katex--inline\">N(k)</span>  be the number of factors of  <span class=\"katex--inline\">2</span>  in the prime factorization of  <span class=\"katex--inline\">I_k</span> .  What is the maximum value of  <span class=\"katex--inline\">N(k)</span> ?</p>\n<p> <span class=\"katex--inline\">\\mathrm{(A)}\\ 6\n\\qquad\n\\mathrm{(B)}\\ 7\n\\qquad\n\\mathrm{(C)}\\ 8\n\\qquad\n\\mathrm{(D)}\\ 9\n\\qquad\n\\mathrm{(E)}\\ 10</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": 4, "problem_name": "2009 AMC 10A Problem 25", "can_next": false, "can_prev": true, "nxt": "", "prev": "/problem/09_amc10A_p24"}}