{"status": "success", "data": {"description_md": "Let $A=\\{1,2,3,4\\}$, and $f$ and $g$ be randomly chosen (not necessarily distinct) functions from $A$ to $A$. The probability that the range of $f$ and the range of $g$ are disjoint is $\\tfrac{m}{n}$, where $m$ and $n$ are relatively prime positive integers. Find $m$.\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=\\{1,2,3,4\\}</span>, and <span class=\"katex--inline\">f</span> and <span class=\"katex--inline\">g</span> be randomly chosen (not necessarily distinct) functions from <span class=\"katex--inline\">A</span> to <span class=\"katex--inline\">A</span>. The probability that the range of <span class=\"katex--inline\">f</span> and the range of <span class=\"katex--inline\">g</span> are disjoint is <span class=\"katex--inline\">\\tfrac{m}{n}</span>, where <span class=\"katex--inline\">m</span> and <span class=\"katex--inline\">n</span> are relatively prime positive integers. Find <span class=\"katex--inline\">m</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": "2014 AIME I Problem 12", "can_next": true, "can_prev": true, "nxt": "/problem/14_aime_I_p13", "prev": "/problem/14_aime_I_p11"}}