{"status": "success", "data": {"description_md": "Suppose $r$ is a real number for which $$ \\left\\lfloor r + \\frac{19}{100} \\right\\rfloor + \\left\\lfloor r + \\frac{20}{100} \\right\\rfloor + \\left\\lfloor r + \\frac{21}{100} \\right\\rfloor + \\cdots + \\left\\lfloor r + \\frac{91}{100} \\right\\rfloor = 546. $$ Find $\\lfloor 100r \\rfloor$. (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>Suppose <span class=\"katex--inline\">r</span> is a real number for which <span class=\"katex--display\"> \\left\\lfloor r + \\frac{19}{100} \\right\\rfloor + \\left\\lfloor r + \\frac{20}{100} \\right\\rfloor + \\left\\lfloor r + \\frac{21}{100} \\right\\rfloor + \\cdots + \\left\\lfloor r + \\frac{91}{100} \\right\\rfloor = 546. </span> Find <span class=\"katex--inline\">\\lfloor 100r \\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": 4, "problem_name": "1991 AIME Problem 6", "can_next": true, "can_prev": true, "nxt": "/problem/91_aime_p07", "prev": "/problem/91_aime_p05"}}