{"status": "success", "data": {"description_md": "The set $G$ is defined by the points $(x,y)$ with integer coordinates, $3\\le|x|\\le7$, $3\\le|y|\\le7$. How many squares of side length at least $6$ have their four vertices in $G$?<br><center><img class=\"problem-image\" alt='[asy] defaultpen(black+0.75bp+fontsize(8pt)); size(5cm); path p = scale(.15)*unitcircle; draw((-8,0)--(8.5,0),Arrow(HookHead,1mm)); draw((0,-8)--(0,8.5),Arrow(HookHead,1mm)); int i,j; for (i=-7;i&lt;8;++i) { for (j=-7;j&lt;8;++j) { if (((-7 &lt;= i) &amp;&amp; (i &lt;= -3)) || ((3 &lt;= i) &amp;&amp;  (i&lt;= 7))) { if (((-7 &lt;= j) &amp;&amp; (j &lt;= -3)) || ((3 &lt;= j) &amp;&amp;  (j&lt;= 7))) { fill(shift(i,j)*p,black); }}}} draw((-7,-.2)--(-7,.2),black+0.5bp); draw((-3,-.2)--(-3,.2),black+0.5bp); draw((3,-.2)--(3,.2),black+0.5bp); draw((7,-.2)--(7,.2),black+0.5bp); draw((-.2,-7)--(.2,-7),black+0.5bp); draw((-.2,-3)--(.2,-3),black+0.5bp); draw((-.2,3)--(.2,3),black+0.5bp); draw((-.2,7)--(.2,7),black+0.5bp); label(\"$-7$\",(-7,0),S); label(\"$-3$\",(-3,0),S); label(\"$3$\",(3,0),S); label(\"$7$\",(7,0),S); label(\"$-7$\",(0,-7),W); label(\"$-3$\",(0,-3),W); label(\"$3$\",(0,3),W); label(\"$7$\",(0,7),W); [/asy]' class=\"latexcenter\" height=\"500\" src=\"https://latex.artofproblemsolving.com/6/9/9/6992511f7ecca62a842cd810c131a3730f9032a8.png\" width=\"500\"/></center>$\\textbf{(A)}\\ 125\\qquad \\textbf{(B)}\\ 150\\qquad \\textbf{(C)}\\ 175\\qquad \\textbf{(D)}\\ 200\\qquad \\textbf{(E)}\\ 225$\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>The set <span class=\"katex--inline\">G</span> is defined by the points <span class=\"katex--inline\">(x,y)</span> with integer coordinates, <span class=\"katex--inline\">3\\le|x|\\le7</span>, <span class=\"katex--inline\">3\\le|y|\\le7</span>. How many squares of side length at least <span class=\"katex--inline\">6</span> have their four vertices in <span class=\"katex--inline\">G</span>?<br/><center><img class=\"latexcenter\" alt=\"[asy] defaultpen(black+0.75bp+fontsize(8pt)); size(5cm); path p = scale(.15)*unitcircle; draw((-8,0)--(8.5,0),Arrow(HookHead,1mm)); draw((0,-8)--(0,8.5),Arrow(HookHead,1mm)); int i,j; for (i=-7;i&lt;8;++i) { for (j=-7;j&lt;8;++j) { if (((-7 &lt;= i) &amp;&amp; (i &lt;= -3)) || ((3 &lt;= i) &amp;&amp;  (i&lt;= 7))) { if (((-7 &lt;= j) &amp;&amp; (j &lt;= -3)) || ((3 &lt;= j) &amp;&amp;  (j&lt;= 7))) { fill(shift(i,j)*p,black); }}}} draw((-7,-.2)--(-7,.2),black+0.5bp); draw((-3,-.2)--(-3,.2),black+0.5bp); draw((3,-.2)--(3,.2),black+0.5bp); draw((7,-.2)--(7,.2),black+0.5bp); draw((-.2,-7)--(.2,-7),black+0.5bp); draw((-.2,-3)--(.2,-3),black+0.5bp); draw((-.2,3)--(.2,3),black+0.5bp); draw((-.2,7)--(.2,7),black+0.5bp); label(&#34;$-7$&#34;,(-7,0),S); label(&#34;$-3$&#34;,(-3,0),S); label(&#34;$3$&#34;,(3,0),S); label(&#34;$7$&#34;,(7,0),S); label(&#34;$-7$&#34;,(0,-7),W); label(&#34;$-3$&#34;,(0,-3),W); label(&#34;$3$&#34;,(0,3),W); label(&#34;$7$&#34;,(0,7),W); [/asy]\" height=\"500\" src=\"https://latex.artofproblemsolving.com/6/9/9/6992511f7ecca62a842cd810c131a3730f9032a8.png\" width=\"500\"/></center><span class=\"katex--inline\">\\textbf{(A)}\\ 125\\qquad \\textbf{(B)}\\ 150\\qquad \\textbf{(C)}\\ 175\\qquad \\textbf{(D)}\\ 200\\qquad \\textbf{(E)}\\ 225</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": 5, "problem_name": "2009 AMC 12B Problem 25", "can_next": false, "can_prev": true, "nxt": "", "prev": "/problem/09_amc12B_p24"}}