{"status": "success", "data": {"description_md": "Find the number of collections of $16$ distinct subsets of $\\{1, 2, 3, 4, 5\\}$ with the property that for any two subsets $X$ and $Y$ in the collection, $X\\cap Y \\neq \\emptyset$.\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>Find the number of collections of <span class=\"katex--inline\">16</span> distinct subsets of <span class=\"katex--inline\">\\{1, 2, 3, 4, 5\\}</span> with the property that for any two subsets <span class=\"katex--inline\">X</span> and <span class=\"katex--inline\">Y</span> in the collection, <span class=\"katex--inline\">X\\cap Y \\neq \\emptyset</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": 5, "problem_name": "2023 AIME II Problem 11", "can_next": true, "can_prev": true, "nxt": "/problem/23_aime_II_p12", "prev": "/problem/23_aime_II_p10"}}