{"status": "success", "data": {"description_md": "Let $S$ be a set with six elements. In how many different ways can one select two not necessarily distinct subsets of $S$ so that the union of the two subsets is $S$? The order of selection does not matter; for example, the pair of subsets $\\{a, c\\}$, $\\{b, c, d, e, f\\}$ represents the same selection as the pair $\\{b, c, d, e, f\\}$, $\\{a, c\\}$.\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\">S</span> be a set with six elements. In how many different ways can one select two not necessarily distinct subsets of <span class=\"katex--inline\">S</span> so that the union of the two subsets is <span class=\"katex--inline\">S</span>? The order of selection does not matter; for example, the pair of subsets <span class=\"katex--inline\">\\{a, c\\}</span>, <span class=\"katex--inline\">\\{b, c, d, e, f\\}</span> represents the same selection as the pair <span class=\"katex--inline\">\\{b, c, d, e, f\\}</span>, <span class=\"katex--inline\">\\{a, c\\}</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": "1993 AIME Problem 8", "can_next": true, "can_prev": true, "nxt": "/problem/93_aime_p09", "prev": "/problem/93_aime_p07"}}