{"status": "success", "data": {"description_md": "Find the number of functions $f$ from $\\{0,1,2,3,4,5,6\\}$ to the integers such that $f(0)=0, f(6)=12$, and<br>\n$$|x-y| \\le |f(x)-f(y)| \\le 3 |x-y| $$for all $x$ and $y$ in $\\{0,1,2,3,4,5,6\\}$.\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>Find the number of functions <span class=\"katex--inline\">f</span> from <span class=\"katex--inline\">\\{0,1,2,3,4,5,6\\}</span> to the integers such that <span class=\"katex--inline\">f(0)=0, f(6)=12</span>, and<br/><span class=\"katex--display\">|x-y| \\le |f(x)-f(y)| \\le 3 |x-y| </span>for all <span class=\"katex--inline\">x</span> and <span class=\"katex--inline\">y</span> in <span class=\"katex--inline\">\\{0,1,2,3,4,5,6\\}</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": 6, "problem_name": "2018 AIME II Problem 15", "can_next": false, "can_prev": true, "nxt": "", "prev": "/problem/18_aime_II_p14"}}