{"status": "success", "data": {"description_md": "A scanning code consists of a $7 \\times 7$ grid of squares, with some of its squares colored black and the rest colored white. There must be at least one square of each color in this grid of $49$ squares. A scanning code is called $\\textit{symmetric}$ if its look does not change when the entire square is rotated by a multiple of $90 ^{\\circ}$ counterclockwise around its center, nor when it is reflected across a line joining opposite corners or a line joining midpoints of opposite sides. What is the total number of possible symmetric scanning codes?\n\n$\\textbf{(A)} \\text{ 510} \\qquad \\textbf{(B)} \\text{ 1022} \\qquad \\textbf{(C)} \\text{ 8190} \\qquad \\textbf{(D)} \\text{ 8192} \\qquad \\textbf{(E)} \\text{ 65,534}$\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>A scanning code consists of a  <span class=\"katex--inline\">7 \\times 7</span>  grid of squares, with some of its squares colored black and the rest colored white. There must be at least one square of each color in this grid of  <span class=\"katex--inline\">49</span>  squares. A scanning code is called  <span class=\"katex--inline\">\\textit{symmetric}</span>  if its look does not change when the entire square is rotated by a multiple of  <span class=\"katex--inline\">90 ^{\\circ}</span>  counterclockwise around its center, nor when it is reflected across a line joining opposite corners or a line joining midpoints of opposite sides. What is the total number of possible symmetric scanning codes?</p>&#10;<p> <span class=\"katex--inline\">\\textbf{(A)} \\text{ 510} \\qquad \\textbf{(B)} \\text{ 1022} \\qquad \\textbf{(C)} \\text{ 8190} \\qquad \\textbf{(D)} \\text{ 8192} \\qquad \\textbf{(E)} \\text{ 65,534}</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": "2018 AMC 12A Problem 15", "can_next": true, "can_prev": true, "nxt": "/problem/18_amc12A_p16", "prev": "/problem/18_amc12A_p14"}}