{"status": "success", "data": {"description_md": "Suppose $a$, $b$ and $c$ are positive integers with $a+b+c=2006$, and $a!b!c!=m\\cdot 10^n$, where $m$ and $n$ are integers and $m$ is not divisible by $10$. What is the smallest possible value of $n$?\n\n$\\mathrm{(A)}\\ 489<br>\\qquad<br>\\mathrm{(B)}\\ 492 <br>\\qquad<br>\\mathrm{(C)}\\ 495<br>\\qquad<br>\\mathrm{(D)}\\ 498<br>\\qquad<br>\\mathrm{(E)}\\ 501$\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>Suppose  <span class=\"katex--inline\">a</span> ,  <span class=\"katex--inline\">b</span>  and  <span class=\"katex--inline\">c</span>  are positive integers with  <span class=\"katex--inline\">a+b+c=2006</span> , and  <span class=\"katex--inline\">a!b!c!=m\\cdot 10^n</span> , where  <span class=\"katex--inline\">m</span>  and  <span class=\"katex--inline\">n</span>  are integers and  <span class=\"katex--inline\">m</span>  is not divisible by  <span class=\"katex--inline\">10</span> . What is the smallest possible value of  <span class=\"katex--inline\">n</span> ?</p>&#10;<p> <span class=\"katex--inline\">\\mathrm{(A)}\\ 489\\qquad\\mathrm{(B)}\\ 492 \\qquad\\mathrm{(C)}\\ 495\\qquad\\mathrm{(D)}\\ 498\\qquad\\mathrm{(E)}\\ 501</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": "2006 AMC 12B Problem 22", "can_next": true, "can_prev": true, "nxt": "/problem/06_amc12B_p23", "prev": "/problem/06_amc12B_p21"}}