{"status": "success", "data": {"description_md": "For each positive integer $n$, let $f(n)$ be the sum of the digits in the base-four representation of $n$ and let $g(n)$ be the sum of the digits in the base-eight representation of $f(n)$. For example, $f(2020) = f(133210_\\text{four}) = 10 = 12_\\text{eight}$, and $g(2020) = \\text{the digit sum of } 12_\\text{eight} = 3$. Let $N$ be the least value of $n$ such that the base-sixteen representation of $g(n)$ cannot be expressed using only the digits $0$ through $9.$ 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>For each positive integer <span class=\"katex--inline\">n</span>, let <span class=\"katex--inline\">f(n)</span> be the sum of the digits in the base-four representation of <span class=\"katex--inline\">n</span> and let <span class=\"katex--inline\">g(n)</span> be the sum of the digits in the base-eight representation of <span class=\"katex--inline\">f(n)</span>. For example, <span class=\"katex--inline\">f(2020) = f(133210_\\text{four}) = 10 = 12_\\text{eight}</span>, and <span class=\"katex--inline\">g(2020) = \\text{the digit sum of } 12_\\text{eight} = 3</span>. Let <span class=\"katex--inline\">N</span> be the least value of <span class=\"katex--inline\">n</span> such that the base-sixteen representation of <span class=\"katex--inline\">g(n)</span> cannot be expressed using only the digits <span class=\"katex--inline\">0</span> through <span class=\"katex--inline\">9.</span> 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": 3, "problem_name": "2020 AIME II Problem 5", "can_next": true, "can_prev": true, "nxt": "/problem/20_aime_II_p06", "prev": "/problem/20_aime_II_p04"}}