{"status": "success", "data": {"description_md": "In the figure below, $3$ of the $6$ disks are to be painted blue, $2$ are to be painted red, and $1$ is to be painted green. Two paintings that can be obtained from one another by a rotation or a reflection of the entire figure are considered the same. How many different paintings are possible?<br><center><img class=\"problem-image\" alt=\"[asy] size(100); pair A, B, C, D, E, F; A = (0,0); B = (1,0); C = (2,0); D = rotate(60, A)*B; E = B + D; F = rotate(60, A)*C; draw(Circle(A, 0.5)); draw(Circle(B, 0.5)); draw(Circle(C, 0.5)); draw(Circle(D, 0.5)); draw(Circle(E, 0.5)); draw(Circle(F, 0.5)); [/asy]\" class=\"latexcenter\" height=\"155\" src=\"https://latex.artofproblemsolving.com/e/b/a/eba8bbf32167d960fbb94db72325cb3a2f89c234.png\" width=\"168\"/></center>\n\n$\\textbf{(A) } 6 \\qquad \\textbf{(B) } 8 \\qquad \\textbf{(C) } 9 \\qquad \\textbf{(D) } 12 \\qquad \\textbf{(E) } 15$\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>In the figure below,  <span class=\"katex--inline\">3</span>  of the  <span class=\"katex--inline\">6</span>  disks are to be painted blue,  <span class=\"katex--inline\">2</span>  are to be painted red, and  <span class=\"katex--inline\">1</span>  is to be painted green. Two paintings that can be obtained from one another by a rotation or a reflection of the entire figure are considered the same. How many different paintings are possible?<br/><center><img class=\"latexcenter\" alt=\"[asy] size(100); pair A, B, C, D, E, F; A = (0,0); B = (1,0); C = (2,0); D = rotate(60, A)*B; E = B + D; F = rotate(60, A)*C; draw(Circle(A, 0.5)); draw(Circle(B, 0.5)); draw(Circle(C, 0.5)); draw(Circle(D, 0.5)); draw(Circle(E, 0.5)); draw(Circle(F, 0.5)); [/asy]\" height=\"155\" src=\"https://latex.artofproblemsolving.com/e/b/a/eba8bbf32167d960fbb94db72325cb3a2f89c234.png\" width=\"168\"/></center></p>&#10;<p> <span class=\"katex--inline\">\\textbf{(A) } 6 \\qquad \\textbf{(B) } 8 \\qquad \\textbf{(C) } 9 \\qquad \\textbf{(D) } 12 \\qquad \\textbf{(E) } 15</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": "2017 AMC 12B Problem 13", "can_next": true, "can_prev": true, "nxt": "/problem/17_amc12B_p14", "prev": "/problem/17_amc12B_p12"}}