{"status": "success", "data": {"description_md": "For any finite set $S$, let $|S|$ denote the number of elements in $S$. FInd the number of ordered pairs $(A,B)$ such that $A$ and $B$ are (not necessarily distinct) subsets of $\\{1,2,3,4,5\\}$ that satisfy<br>\n$$|A| \\cdot |B| = |A \\cap B| \\cdot |A \\cup B| $$\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>For any finite set <span class=\"katex--inline\">S</span>, let <span class=\"katex--inline\">|S|</span> denote the number of elements in <span class=\"katex--inline\">S</span>. FInd the number of ordered pairs <span class=\"katex--inline\">(A,B)</span> such that <span class=\"katex--inline\">A</span> and <span class=\"katex--inline\">B</span> are (not necessarily distinct) subsets of <span class=\"katex--inline\">\\{1,2,3,4,5\\}</span> that satisfy<br/><span class=\"katex--display\">|A| \\cdot |B| = |A \\cap B| \\cdot |A \\cup B|</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": "2021 AIME II Problem 6", "can_next": true, "can_prev": true, "nxt": "/problem/21_aime_II_p07", "prev": "/problem/21_aime_II_p05"}}