{"status": "success", "data": {"description_md": "The diagram below shows a $ 4\\times4$ rectangular array of points, each of which is $ 1$ unit away from its nearest neighbors.<br>$\\includegraphics[width=49, height=49, totalheight=49]{https://latex.artofproblemsolving.com/6/9/2/692afb290d742c3d6e127cace41bce146431ca05.png}$Define a growing path to be a sequence of distinct points of the array with the property that the distance between consecutive points of the sequence is strictly increasing. Let $ m$ be the maximum possible number of points in a growing path, and let $ r$ be the number of growing paths consisting of exactly $ m$ points. Find $ mr$.\n___\nLeading zeroes must be inputted, so if your answer is `34`, then input `034`. Full 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 diagram below shows a $ 4\\times4$ rectangular array of points, each of which is $ 1$ unit away from its nearest neighbors.<br/><img src=\"https://latex.artofproblemsolving.com/6/9/2/692afb290d742c3d6e127cace41bce146431ca05.png\" width=\"49\" height=\"49\" class=\"problem-image\"/>Define a growing path to be a sequence of distinct points of the array with the property that the distance between consecutive points of the sequence is strictly increasing. Let $ m$ be the maximum possible number of points in a growing path, and let $ r$ be the number of growing paths consisting of exactly $ m$ points. Find $ mr$.</p>&#10;<hr><p>Leading zeroes must be inputted, so if your answer is <code>34</code>, then input <code>034</code>. 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": 5, "problem_name": "2008 AIME II Problem 10", "can_next": true, "can_prev": true, "nxt": "/problem/08_aime_II_p11", "prev": "/problem/08_aime_II_p09"}}