{"status": "success", "data": {"description_md": "How many of the first 1000 positive integers can be expressed in the form<br>\n$$ \\lfloor 2x \\rfloor + \\lfloor 4x \\rfloor + \\lfloor 6x \\rfloor + \\lfloor 8x \\rfloor, $$ where $x$ is a real number, and $\\lfloor z \\rfloor$ denotes the greatest integer less than or equal to $z$?\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>How many of the first 1000 positive integers can be expressed in the form<br/><span class=\"katex--display\"> \\lfloor 2x \\rfloor + \\lfloor 4x \\rfloor + \\lfloor 6x \\rfloor + \\lfloor 8x \\rfloor, </span><br/>where <span class=\"katex--inline\">x</span> is a real number, and <span class=\"katex--inline\">\\lfloor z \\rfloor</span> denotes the greatest integer less than or equal to <span class=\"katex--inline\">z</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": 5, "problem_name": "1985 AIME Problem 10", "can_next": true, "can_prev": true, "nxt": "/problem/85_aime_p11", "prev": "/problem/85_aime_p09"}}