{"status": "success", "data": {"description_md": "Let $S$ be the increasing sequence of positive integers whose binary representation has exactly $8$ ones. Let $N$ be the $1000^{th}$ number in $S$. 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\">S</span> be the increasing sequence of positive integers whose binary representation has exactly <span class=\"katex--inline\">8</span> ones. Let <span class=\"katex--inline\">N</span> be the <span class=\"katex--inline\">1000^{th}</span> number in <span class=\"katex--inline\">S</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": 4, "problem_name": "2012 AIME II Problem 7", "can_next": true, "can_prev": true, "nxt": "/problem/12_aime_II_p08", "prev": "/problem/12_aime_II_p06"}}