{"status": "success", "data": {"description_md": "A rectangular piece of of paper measures 4 units by 5 units. Several lines are drawn parallel to the edges of the paper. A rectangle determined by the intersections of some of these lines is called basic if<br><br>(i) all four sides of the rectangle are segments of drawn line segments, and<br>(ii) no segments of drawn lines lie inside the rectangle.<br><br>Given that the total length of all lines drawn is exactly 2007 units, let $N$ be the maximum possible number of basic rectangles determined. Find the remainder when $N$ is divided by 1000.\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>A rectangular piece of of paper measures 4 units by 5 units. Several lines are drawn parallel to the edges of the paper. A rectangle determined by the intersections of some of these lines is called basic if<br/><br/>(i) all four sides of the rectangle are segments of drawn line segments, and<br/>(ii) no segments of drawn lines lie inside the rectangle.<br/><br/>Given that the total length of all lines drawn is exactly 2007 units, let <span class=\"katex--inline\">N</span> be the maximum possible number of basic rectangles determined. Find the remainder when <span class=\"katex--inline\">N</span> is divided by 1000.</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": 4, "problem_name": "2007 AIME II Problem 8", "can_next": true, "can_prev": true, "nxt": "/problem/07_aime_II_p09", "prev": "/problem/07_aime_II_p07"}}