{"status": "success", "data": {"description_md": "Let $m$ be the number of five-element subsets that can be chosen from the set of the first $14$ natural numbers so that at least two of the five numbers are consecutive. Find the remainder when $m$ 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\">m</span> be the number of five-element subsets that can be chosen from the set of the first <span class=\"katex--inline\">14</span> natural numbers so that at least two of the five numbers are consecutive. Find the remainder when <span class=\"katex--inline\">m</span> is divided by <span class=\"katex--inline\">1000</span>.</p>&#10;<hr/>&#10;<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>&#10;", "hints_md": "", "hints_html": "", "editorial_md": "", "editorial_html": "", "flag_hint": "", "point_value": 4, "problem_name": "2009 AIME II Problem 6", "can_next": true, "can_prev": true, "nxt": "/problem/09_aime_II_p07", "prev": "/problem/09_aime_II_p05"}}