{"status": "success", "data": {"description_md": "Let $N$ be the number of positive integers that are less than or equal to 2003 and whose base-2 representation has more 1's than 0'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\">N</span> be the number of positive integers that are less than or equal to 2003 and whose base-2 representation has more 1&#8217;s than 0&#8217;s. Find the remainder when <span class=\"katex--inline\">N</span> is divided by 1000.</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": "2003 AIME I Problem 13", "can_next": true, "can_prev": true, "nxt": "/problem/03_aime_I_p14", "prev": "/problem/03_aime_I_p12"}}