{"status": "success", "data": {"description_md": "Patio blocks that are hexagons $1$ unit on a side are used to outline a garden by placing the blocks edge to edge with $n$ on each side. The diagram indicates the path of blocks around the garden when $n=5.$<br><br>$\\includegraphics[width=187, height=209, totalheight=209]{https://latex.artofproblemsolving.com/f/4/5/f45f1f77bdff40394c61710ee6269964bef583ba.png}$<br>If $n=202,$ then the area of the garden enclosed by the path, not including the path itself, is $m(\\sqrt{3}/2)$ square units, where $m$ is a positive integer. Find the remainder when $m$ 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>Patio blocks that are hexagons <span class=\"katex--inline\">1</span> unit on a side are used to outline a garden by placing the blocks edge to edge with <span class=\"katex--inline\">n</span> on each side. The diagram indicates the path of blocks around the garden when <span class=\"katex--inline\">n=5.</span><br/><br/><img src=\"https://latex.artofproblemsolving.com/f/4/5/f45f1f77bdff40394c61710ee6269964bef583ba.png\" width=\"187\" height=\"209\" class=\"problem-image\"/><br/>If <span class=\"katex--inline\">n=202,</span> then the area of the garden enclosed by the path, not including the path itself, is <span class=\"katex--inline\">m(\\sqrt{3}/2)</span> square units, where <span class=\"katex--inline\">m</span> is a positive integer. Find the remainder when <span class=\"katex--inline\">m</span> is divided by <span class=\"katex--inline\">1000.</span></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": 3, "problem_name": "2002 AIME II Problem 4", "can_next": true, "can_prev": true, "nxt": "/problem/02_aime_II_p05", "prev": "/problem/02_aime_II_p03"}}