{"status": "success", "data": {"description_md": "As shown in the figure below, a regular dodecahedron (the polyhedron consisting of $12$ congruent regular pentagonal faces) floats in empty space with two horizontal faces. Note that there is a ring of five slanted faces adjacent to the top face, and a ring of five slanted faces adjacent to the bottom face. How many ways are there to move from the top face to the bottom face via a sequence of adjacent faces so that each face is visited at most once and moves are not permitted from the bottom ring to the top ring?\n\n<center>\n<img class=\"problem-image\" height=\"205\" src=\"https://latex.artofproblemsolving.com/0/8/5/08541e5d1cec59e7dd49ea0bbdb45fe328dbecbb.png\" width=\"202\"/>\n</center><br>\n\n$\\textbf{(A) } 125 \\qquad \\textbf{(B) } 250 \\qquad \\textbf{(C) } 405 \\qquad \\textbf{(D) } 640 \\qquad \\textbf{(E) } 810$", "description_html": "<p>As shown in the figure below, a regular dodecahedron (the polyhedron consisting of <span class=\"katex--inline\">12</span> congruent regular pentagonal faces) floats in empty space with two horizontal faces. Note that there is a ring of five slanted faces adjacent to the top face, and a ring of five slanted faces adjacent to the bottom face. How many ways are there to move from the top face to the bottom face via a sequence of adjacent faces so that each face is visited at most once and moves are not permitted from the bottom ring to the top ring?</p>&#10;<center>&#10;<img class=\"problem-image\" height=\"205\" src=\"https://latex.artofproblemsolving.com/0/8/5/08541e5d1cec59e7dd49ea0bbdb45fe328dbecbb.png\" width=\"202\"/>&#10;</center><br/>&#10;<p><span class=\"katex--inline\">\\textbf{(A) } 125 \\qquad \\textbf{(B) } 250 \\qquad \\textbf{(C) } 405 \\qquad \\textbf{(D) } 640 \\qquad \\textbf{(E) } 810</span></p>&#10;", "hints_md": "", "hints_html": "", "editorial_md": "", "editorial_html": "", "flag_hint": "", "point_value": 3, "problem_name": "2020 AMC 10A Problem 19", "can_next": true, "can_prev": true, "nxt": "/problem/20_amc10A_p20", "prev": "/problem/20_amc10A_p18"}}