{"status": "success", "data": {"description_md": "A sample of 121 integers is given, each between 1 and 1000 inclusive, with repetitions allowed. The sample has a unique mode (most frequent value). Let $D$ be the difference between the mode and the arithmetic mean of the sample. What is the largest possible value of $\\lfloor D\\rfloor$? (For real $x$, $\\lfloor x\\rfloor$ is the greatest integer less than or equal to $x$.)\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 sample of 121 integers is given, each between 1 and 1000 inclusive, with repetitions allowed. The sample has a unique mode (most frequent value). Let <span class=\"katex--inline\">D</span> be the difference between the mode and the arithmetic mean of the sample. What is the largest possible value of <span class=\"katex--inline\">\\lfloor D\\rfloor</span>? (For real <span class=\"katex--inline\">x</span>, <span class=\"katex--inline\">\\lfloor x\\rfloor</span> is the greatest integer less than or equal to <span class=\"katex--inline\">x</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": "1989 AIME Problem 11", "can_next": true, "can_prev": true, "nxt": "/problem/89_aime_p12", "prev": "/problem/89_aime_p10"}}