{"status": "success", "data": {"description_md": "A certain function $f$ has the properties that $f(3x)=3f(x)$ for all positive real values of $x$, and that $f(x)=1-\\mid x-2 \\mid$ for $1\\leq x \\leq 3$. Find the smallest $x$ for which $f(x)=f(2001)$.\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 certain function <span class=\"katex--inline\">f</span> has the properties that <span class=\"katex--inline\">f(3x)=3f(x)</span> for all positive real values of <span class=\"katex--inline\">x</span>, and that <span class=\"katex--inline\">f(x)=1-\\mid x-2 \\mid</span> for <span class=\"katex--inline\">1\\leq x \\leq 3</span>. Find the smallest <span class=\"katex--inline\">x</span> for which <span class=\"katex--inline\">f(x)=f(2001)</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": 4, "problem_name": "2001 AIME II Problem 8", "can_next": true, "can_prev": true, "nxt": "/problem/01_aime_II_p09", "prev": "/problem/01_aime_II_p07"}}