{"status": "success", "data": {"description_md": "Aaron the ant walks on the coordinate plane according to the following rules. He starts at the origin $p_0=(0,0)$ facing to the east and walks one unit, arriving at $p_1=(1,0)$. For $n=1,2,3,\\dots$, right after arriving at the point $p_n$, if Aaron can turn $90^\\circ$ left and walk one unit to an unvisited point $p_{n+1}$, he does that. Otherwise, he walks one unit straight ahead to reach $p_{n+1}$. Thus the sequence of points continues $p_2=(1,1), p_3=(0,1), p_4=(-1,1), p_5=(-1,0)$, and so on in a counterclockwise spiral pattern. What is $p_{2015}$?\n\n$\\textbf{(A) } (-22,-13)\\qquad\\textbf{(B) } (-13,-22)\\qquad\\textbf{(C) } (-13,22)\\qquad\\textbf{(D) } (13,-22)\\qquad\\textbf{(E) } (22,-13)$", "description_html": "<p>Aaron the ant walks on the coordinate plane according to the following rules. He starts at the origin  <span class=\"katex--inline\">p_0=(0,0)</span>  facing to the east and walks one unit, arriving at  <span class=\"katex--inline\">p_1=(1,0)</span> . For  <span class=\"katex--inline\">n=1,2,3,\\dots</span> , right after arriving at the point  <span class=\"katex--inline\">p_n</span> , if Aaron can turn  <span class=\"katex--inline\">90^\\circ</span>  left and walk one unit to an unvisited point  <span class=\"katex--inline\">p_{n+1}</span> , he does that. Otherwise, he walks one unit straight ahead to reach  <span class=\"katex--inline\">p_{n+1}</span> . Thus the sequence of points continues  <span class=\"katex--inline\">p_2=(1,1), p_3=(0,1), p_4=(-1,1), p_5=(-1,0)</span> , and so on in a counterclockwise spiral pattern. What is  <span class=\"katex--inline\">p_{2015}</span> ?</p>\n<p> <span class=\"katex--inline\">\\textbf{(A) } (-22,-13)\\qquad\\textbf{(B) } (-13,-22)\\qquad\\textbf{(C) } (-13,22)\\qquad\\textbf{(D) } (13,-22)\\qquad\\textbf{(E) } (22,-13)</span> </p>\n<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": 4, "problem_name": "2015 AMC 10B Problem 24", "can_next": true, "can_prev": true, "nxt": "/problem/15_amc10B_p25", "prev": "/problem/15_amc10B_p23"}}