{"status": "success", "data": {"description_md": "Let $\\mathcal{S}$ be the set $\\{1,2,3,\\ldots,10\\}.$ Let $n$ be the number of sets of two non-empty disjoint subsets of $\\mathcal{S}.$ (Disjoint sets are defined as sets that have no common elements.) Find the remainder obtained 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>Let <span class=\"katex--inline\">\\mathcal{S}</span> be the set <span class=\"katex--inline\">\\{1,2,3,\\ldots,10\\}.</span> Let <span class=\"katex--inline\">n</span> be the number of sets of two non-empty disjoint subsets of <span class=\"katex--inline\">\\mathcal{S}.</span> (Disjoint sets are defined as sets that have no common elements.) Find the remainder obtained when <span class=\"katex--inline\">n</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": 4, "problem_name": "2002 AIME II Problem 9", "can_next": true, "can_prev": true, "nxt": "/problem/02_aime_II_p10", "prev": "/problem/02_aime_II_p08"}}