{"status": "success", "data": {"description_md": "Suppose $[a\\ b]$ denotes the average of $a$ and $b$, and $\\{a\\ b\\ c\\}$ denotes the average of $a, b$, and $c$. What is $\\{\\{1\\ 1\\ 0\\}\\ [0\\ 1]\\ 0\\}$?\n\n$\\textbf{(A)}\\ \\frac{2}{9} \\qquad\\textbf{(B)}\\ \\frac{5}{18} \\qquad\\textbf{(C)}\\ \\frac{1}{3} \\qquad\\textbf{(D)}\\ \\frac{7}{18} \\qquad\\textbf{(E)}\\ \\frac{2}{3}$", "description_html": "<p>Suppose  <span class=\"katex--inline\">[a\\ b]</span>  denotes the average of  <span class=\"katex--inline\">a</span>  and  <span class=\"katex--inline\">b</span> , and  <span class=\"katex--inline\">\\{a\\ b\\ c\\}</span>  denotes the average of  <span class=\"katex--inline\">a, b</span> , and  <span class=\"katex--inline\">c</span> . What is  <span class=\"katex--inline\">\\{\\{1\\ 1\\ 0\\}\\ [0\\ 1]\\ 0\\}</span> ?</p>\n<p> <span class=\"katex--inline\">\\textbf{(A)}\\ \\frac{2}{9} \\qquad\\textbf{(B)}\\ \\frac{5}{18} \\qquad\\textbf{(C)}\\ \\frac{1}{3} \\qquad\\textbf{(D)}\\ \\frac{7}{18} \\qquad\\textbf{(E)}\\ \\frac{2}{3}</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": 1, "problem_name": "2011 AMC 10A Problem 3", "can_next": true, "can_prev": true, "nxt": "/problem/11_amc10A_p04", "prev": "/problem/11_amc10A_p02"}}