{"status": "success", "data": {"description_md": "The $\\textit{taxicab distance}$ between points $(x_1, y_1)$ and $(x_2, y_2)$ in the coordinate plane is given by $$|x_1 - x_2| + |y_1 - y_2|.$$<br>For how many points $P$ with integer coordinates is the taxicab distance between $P$ and the origin less than or equal to $20$?\n\n$\\textbf{(A)} \\, 441 \\qquad\\textbf{(B)} \\, 761 \\qquad\\textbf{(C)} \\, 841 \\qquad\\textbf{(D)} \\, 921  \\qquad\\textbf{(E)} \\, 924$\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  <span class=\"katex--inline\">\\textit{taxicab distance}</span>  between points  <span class=\"katex--inline\">(x_1, y_1)</span>  and  <span class=\"katex--inline\">(x_2, y_2)</span>  in the coordinate plane is given by  <span class=\"katex--display\">|x_1 - x_2| + |y_1 - y_2|.</span> <br/>For how many points  <span class=\"katex--inline\">P</span>  with integer coordinates is the taxicab distance between  <span class=\"katex--inline\">P</span>  and the origin less than or equal to  <span class=\"katex--inline\">20</span> ?</p>&#10;<p> <span class=\"katex--inline\">\\textbf{(A)} \\, 441 \\qquad\\textbf{(B)} \\, 761 \\qquad\\textbf{(C)} \\, 841 \\qquad\\textbf{(D)} \\, 921  \\qquad\\textbf{(E)} \\, 924</span> </p>&#10;<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": 2, "problem_name": "2022 AMC 12A Problem 5", "can_next": true, "can_prev": true, "nxt": "/problem/22_amc12A_p06", "prev": "/problem/22_amc12A_p04"}}