{"status": "success", "data": {"description_md": "The numbers 1, 2, 3, 4, 5 are to be arranged in a circle. An arrangement is ''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$\\textbf {(A) } 1 \\qquad \\textbf {(B) } 2 \\qquad \\textbf {(C) } 3 \\qquad \\textbf {(D) } 4 \\qquad \\textbf {(E) } 5$", "description_html": "<p>The numbers 1, 2, 3, 4, 5 are to be arranged in a circle. An arrangement is &#8220;bad&#8221; 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>\n<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>\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": "2014 AMC 10B Problem 24", "can_next": true, "can_prev": true, "nxt": "/problem/14_amc10B_p25", "prev": "/problem/14_amc10B_p23"}}