{"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 *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$\\textbf{(A)} \\text{ 510} \\qquad \\textbf{(B)} \\text{ 1022} \\qquad \\textbf{(C)} \\text{ 8190} \\qquad \\textbf{(D)} \\text{ 8192} \\qquad \\textbf{(E)} \\text{ 65,534}$", "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 <em>symmetric</em> 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;", "hints_md": "", "hints_html": "", "editorial_md": "", "editorial_html": "", "flag_hint": "", "point_value": 3, "problem_name": "2018 AMC 10A Problem 20", "can_next": true, "can_prev": true, "nxt": "/problem/18_amc10A_p21", "prev": "/problem/18_amc10A_p19"}}