{"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.
\n![[asy] unitsize(0.25inch); defaultpen(linewidth(0.7)); int i, j; for(i = 0; i < 4; ++i) for(j = 0; j < 4; ++j) dot(((real)i, (real)j)); [/asy]](https://latex.artofproblemsolving.com/1/6/e/16ed1460ee16eabb872eb9645928df7b6cf2f60a.png)\nDefine 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": "

The diagram below shows a 4\\times4 rectangular array of points, each of which is 1 unit away from its nearest neighbors.

\"[asy]
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.

Leading zeroes must be inputted, so if your answer is 34, then input 034. Full credit goes to MAA for authoring these problems. These problems were taken on the AOPS website.

", "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"}}