{"status": "success", "data": {"description_md": "A game uses a deck of $n$ different cards, where $n$ is an integer and $n \\geq 6$. The number of possible sets of $6$ cards that can be drawn from the deck is $6$ times the number of possible sets of $3$ cards that can be drawn. Find $n$.\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>A game uses a deck of <span class=\"katex--inline\">n</span> different cards, where <span class=\"katex--inline\">n</span> is an integer and <span class=\"katex--inline\">n \\geq 6</span>. The number of possible sets of <span class=\"katex--inline\">6</span> cards that can be drawn from the deck is <span class=\"katex--inline\">6</span> times the number of possible sets of <span class=\"katex--inline\">3</span> cards that can be drawn. Find <span class=\"katex--inline\">n</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": "2005 AIME II Problem 1", "can_next": true, "can_prev": false, "nxt": "/problem/05_aime_II_p02", "prev": ""}}