{"status": "success", "data": {"description_md": "Two different cubes of the same size are to be painted, with the color of each face being chosen independently and at random to be either black or white. What is the probability that after they are painted, the cubes can be rotated to be identical in appearance?\n\n$\\textbf{(A)}\\ \\frac{9}{64} \\qquad\\textbf{(B)}\\ \\frac{289}{2048} \\qquad\\textbf{(C)}\\  \\frac{73}{512} \\qquad\\textbf{(D)}\\ \\frac{147}{1024} \\qquad\\textbf{(E)}\\ \\frac{589}{4096}$\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>Two different cubes of the same size are to be painted, with the color of each face being chosen independently and at random to be either black or white. What is the probability that after they are painted, the cubes can be rotated to be identical in appearance?</p>&#10;<p> <span class=\"katex--inline\">\\textbf{(A)}\\ \\frac{9}{64} \\qquad\\textbf{(B)}\\ \\frac{289}{2048} \\qquad\\textbf{(C)}\\  \\frac{73}{512} \\qquad\\textbf{(D)}\\ \\frac{147}{1024} \\qquad\\textbf{(E)}\\ \\frac{589}{4096}</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": "2020 AMC 12B Problem 20", "can_next": true, "can_prev": true, "nxt": "/problem/20_amc12B_p21", "prev": "/problem/20_amc12B_p19"}}