{"status": "success", "data": {"description_md": "Cities $A$, $B$, $C$, $D$, and $E$ are connected by roads $\\overline{AB}$, $\\overline{AD}$, $\\overline{AE}$, $\\overline{BC}$, $\\overline{BD}$, $\\overline{CD}$, and $\\overline{DE}$. How many different routes are there from $A$ to $B$ that use each road exactly once? (Such a route will necessarily visit some cities more than once.)<br><center><img class=\"problem-image\" alt='[asy] unitsize(10mm); defaultpen(linewidth(1.2pt)+fontsize(10pt)); dotfactor=4; pair A=(1,0), B=(4.24,0), C=(5.24,3.08), D=(2.62,4.98), E=(0,3.08); dot (A); dot (B); dot (C); dot (D); dot (E); label(\"$A$\",A,S); label(\"$B$\",B,SE); label(\"$C$\",C,E); label(\"$D$\",D,N); label(\"$E$\",E,W); guide squiggly(path g, real stepsize, real slope=45) {  real len = arclength(g);  real step = len / round(len / stepsize);  guide squig;  for (real u = 0; u &lt; len; u += step){  real a = arctime(g, u);  real b = arctime(g, u + step / 2);  pair p = point(g, a);  pair q = point(g, b);  pair np = unit( rotate(slope) * dir(g,a));  pair nq = unit( rotate(0 - slope) * dir(g,b));  squig = squig .. p{np} .. q{nq};  }  squig = squig .. point(g, length(g)){unit(rotate(slope)*dir(g,length(g)))};  return squig; } pen pp = defaultpen + 2.718; draw(squiggly(A--B, 4.04, 30), pp); draw(squiggly(A--D, 7.777, 20), pp); draw(squiggly(A--E, 5.050, 15), pp); draw(squiggly(B--C, 5.050, 15), pp); draw(squiggly(B--D, 4.04, 20), pp); draw(squiggly(C--D, 2.718, 20), pp); draw(squiggly(D--E, 2.718, -60), pp); [/asy]' class=\"latexcenter\" height=\"275\" src=\"https://latex.artofproblemsolving.com/c/a/d/cad21e9f9faa2994b8ed3c1a3acfbcc204d0b482.png\" width=\"278\"/></center>\n\n$\\textbf{(A)}\\ 7 \\qquad \\textbf{(B)}\\ 9 \\qquad \\textbf{(C)}\\ 12 \\qquad \\textbf{(D)}\\ 16 \\qquad \\textbf{(E)}\\ 18$\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>Cities <span class=\"katex--inline\">A</span>, <span class=\"katex--inline\">B</span>, <span class=\"katex--inline\">C</span>, <span class=\"katex--inline\">D</span>, and <span class=\"katex--inline\">E</span> are connected by roads <span class=\"katex--inline\">\\overline{AB}</span>, <span class=\"katex--inline\">\\overline{AD}</span>, <span class=\"katex--inline\">\\overline{AE}</span>, <span class=\"katex--inline\">\\overline{BC}</span>, <span class=\"katex--inline\">\\overline{BD}</span>, <span class=\"katex--inline\">\\overline{CD}</span>, and <span class=\"katex--inline\">\\overline{DE}</span>. How many different routes are there from <span class=\"katex--inline\">A</span> to <span class=\"katex--inline\">B</span> that use each road exactly once? (Such a route will necessarily visit some cities more than once.)<br/><center><img class=\"latexcenter\" alt=\"[asy] unitsize(10mm); defaultpen(linewidth(1.2pt)+fontsize(10pt)); dotfactor=4; pair A=(1,0), B=(4.24,0), C=(5.24,3.08), D=(2.62,4.98), E=(0,3.08); dot (A); dot (B); dot (C); dot (D); dot (E); label(&#34;$A$&#34;,A,S); label(&#34;$B$&#34;,B,SE); label(&#34;$C$&#34;,C,E); label(&#34;$D$&#34;,D,N); label(&#34;$E$&#34;,E,W); guide squiggly(path g, real stepsize, real slope=45) {  real len = arclength(g);  real step = len / round(len / stepsize);  guide squig;  for (real u = 0; u &lt; len; u += step){  real a = arctime(g, u);  real b = arctime(g, u + step / 2);  pair p = point(g, a);  pair q = point(g, b);  pair np = unit( rotate(slope) * dir(g,a));  pair nq = unit( rotate(0 - slope) * dir(g,b));  squig = squig .. p{np} .. q{nq};  }  squig = squig .. point(g, length(g)){unit(rotate(slope)*dir(g,length(g)))};  return squig; } pen pp = defaultpen + 2.718; draw(squiggly(A--B, 4.04, 30), pp); draw(squiggly(A--D, 7.777, 20), pp); draw(squiggly(A--E, 5.050, 15), pp); draw(squiggly(B--C, 5.050, 15), pp); draw(squiggly(B--D, 4.04, 20), pp); draw(squiggly(C--D, 2.718, 20), pp); draw(squiggly(D--E, 2.718, -60), pp); [/asy]\" height=\"275\" src=\"https://latex.artofproblemsolving.com/c/a/d/cad21e9f9faa2994b8ed3c1a3acfbcc204d0b482.png\" width=\"278\"/></center></p>&#10;<p><span class=\"katex--inline\">\\textbf{(A)}\\ 7 \\qquad \\textbf{(B)}\\ 9 \\qquad \\textbf{(C)}\\ 12 \\qquad \\textbf{(D)}\\ 16 \\qquad \\textbf{(E)}\\ 18</span></p>&#10;<hr/>&#10;<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>&#10;", "hints_md": "", "hints_html": "", "editorial_md": "", "editorial_html": "", "flag_hint": "", "point_value": 3, "problem_name": "2013 AMC 12B Problem 12", "can_next": true, "can_prev": true, "nxt": "/problem/13_amc12B_p13", "prev": "/problem/13_amc12B_p11"}}