{"status": "success", "data": {"description_md": "A group of children held a grape-eating contest. When the contest was over, the winner had eaten $n$ grapes, and the child in $k$th place had eaten $n+2-2k$ grapes. The total number of grapes eaten in the contest was $2009$. Find the smallest possible value of $n$.\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 group of children held a grape-eating contest. When the contest was over, the winner had eaten <span class=\"katex--inline\">n</span> grapes, and the child in <span class=\"katex--inline\">k</span>th place had eaten <span class=\"katex--inline\">n+2-2k</span> grapes. The total number of grapes eaten in the contest was <span class=\"katex--inline\">2009</span>. Find the smallest possible value of <span class=\"katex--inline\">n</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": 3, "problem_name": "2009 AIME II Problem 4", "can_next": true, "can_prev": true, "nxt": "/problem/09_aime_II_p05", "prev": "/problem/09_aime_II_p03"}}