{"status": "success", "data": {"description_md": "Let $A = \\left\\{ 1,2,3,4,5,6,7 \\right\\}$ and let $N$ be the number of functions $f$ from set $A$ to set $A$ such that $f(f(x))$ is a constant function. Find the remainder when $N$ 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\">A = \\left\\{ 1,2,3,4,5,6,7 \\right\\}</span> and let <span class=\"katex--inline\">N</span> be the number of functions <span class=\"katex--inline\">f</span> from set <span class=\"katex--inline\">A</span> to set <span class=\"katex--inline\">A</span> such that <span class=\"katex--inline\">f(f(x))</span> is a constant function. Find the remainder when <span class=\"katex--inline\">N</span> is divided by <span class=\"katex--inline\">1000</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": "2013 AIME II Problem 11", "can_next": true, "can_prev": true, "nxt": "/problem/13_aime_II_p12", "prev": "/problem/13_aime_II_p10"}}