{"status": "success", "data": {"description_md": "Let $N$ be a positive multiple of $5$. One red ball and $N$ green balls are arranged in a line in random order. Let $P(N)$ be the probability that at least $\\tfrac{3}{5}$ of the green balls are on the same side of the red ball. Observe that $P(5)=1$ and that $P(N)$ approaches $\\tfrac{4}{5}$ as $N$ grows large. What is the sum of the digits of the least value of $N$ such that $P(N) < \\tfrac{321}{400}$?\n\n$\\textbf{(A)}\\ 12\\qquad\\textbf{(B)}\\ 14\\qquad\\textbf{(C)}\\ 16\\qquad\\textbf{(D)}\\ 18\\qquad\\textbf{(E)}\\ 20$\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>Let  <span class=\"katex--inline\">N</span>  be a positive multiple of  <span class=\"katex--inline\">5</span> . One red ball and  <span class=\"katex--inline\">N</span>  green balls are arranged in a line in random order. Let  <span class=\"katex--inline\">P(N)</span>  be the probability that at least  <span class=\"katex--inline\">\\tfrac{3}{5}</span>  of the green balls are on the same side of the red ball. Observe that  <span class=\"katex--inline\">P(5)=1</span>  and that  <span class=\"katex--inline\">P(N)</span>  approaches  <span class=\"katex--inline\">\\tfrac{4}{5}</span>  as  <span class=\"katex--inline\">N</span>  grows large. What is the sum of the digits of the least value of  <span class=\"katex--inline\">N</span>  such that  <span class=\"katex--inline\">P(N) &lt; \\tfrac{321}{400}</span> ?</p>&#10;<p> <span class=\"katex--inline\">\\textbf{(A)}\\ 12\\qquad\\textbf{(B)}\\ 14\\qquad\\textbf{(C)}\\ 16\\qquad\\textbf{(D)}\\ 18\\qquad\\textbf{(E)}\\ 20</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": 3, "problem_name": "2016 AMC 12A Problem 13", "can_next": true, "can_prev": true, "nxt": "/problem/16_amc12A_p14", "prev": "/problem/16_amc12A_p12"}}