{"status": "success", "data": {"description_md": "The numbers $1$, $2$, $3$, $4$, $5$, are to be arranged in a circle.  An arrangement is $\\textit{bad}$ if it is not true that for every $n$ from $1$ to $15$ one can find a subset of the numbers that appear consecutively on the circle that sum to $n$.  Arrangements that differ only by a rotation or a reflection are considered the same.  How many different bad arrangements are there?\n\n$\\textbf{(A) }1\\qquad\\textbf{(B) }2\\qquad\\textbf{(C) }3\\qquad\\textbf{(D) }4\\qquad\\textbf{(E) }5$\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>The numbers  <span class=\"katex--inline\">1</span> ,  <span class=\"katex--inline\">2</span> ,  <span class=\"katex--inline\">3</span> ,  <span class=\"katex--inline\">4</span> ,  <span class=\"katex--inline\">5</span> , are to be arranged in a circle.  An arrangement is  <span class=\"katex--inline\">\\textit{bad}</span>  if it is not true that for every  <span class=\"katex--inline\">n</span>  from  <span class=\"katex--inline\">1</span>  to  <span class=\"katex--inline\">15</span>  one can find a subset of the numbers that appear consecutively on the circle that sum to  <span class=\"katex--inline\">n</span> .  Arrangements that differ only by a rotation or a reflection are considered the same.  How many different bad arrangements are there?</p>&#10;<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>&#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": "2014 AMC 12B Problem 18", "can_next": true, "can_prev": true, "nxt": "/problem/14_amc12B_p19", "prev": "/problem/14_amc12B_p17"}}