{"status": "success", "data": {"description_md": "For each positive integer n, let $f(n) = \\sum_{k = 1}^{100} \\lfloor \\log_{10} (kn) \\rfloor$. Find the largest value of n for which $f(n) \\le 300$.<br><br>Note: $\\lfloor x \\rfloor$ 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>For each positive integer n, let <span class=\"katex--inline\">f(n) = \\sum_{k = 1}^{100} \\lfloor \\log_{10} (kn) \\rfloor</span>. Find the largest value of n for which <span class=\"katex--inline\">f(n) \\le 300</span>.<br/><br/>Note: <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/>&#10;<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>&#10;", "hints_md": "", "hints_html": "", "editorial_md": "", "editorial_html": "", "flag_hint": "", "point_value": 6, "problem_name": "2010 AIME I Problem 14", "can_next": true, "can_prev": true, "nxt": "/problem/10_aime_I_p15", "prev": "/problem/10_aime_I_p13"}}