{"status": "success", "data": {"description_md": "For positive integer $n$, define $S_n$ to be the minimum value of the sum $$ \\sum_{k=1}^n \\sqrt{(2k-1)^2+a_k^2}, $$ where $a_1,a_2,\\ldots,a_n$ are positive real numbers whose sum is 17. There is a unique positive integer $n$ for which $S_n$ is also an integer. Find this $n$.\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": "

For positive integer n, define S_n to be the minimum value of the sum \\sum_{k=1}^n \\sqrt{(2k-1)^2+a_k^2}, where a_1,a_2,\\ldots,a_n are positive real numbers whose sum is 17. There is a unique positive integer n for which S_n is also an integer. Find this n.

Leading zeroes must be inputted, so if your answer is 34, then input 034. Full credit goes to MAA for authoring these problems. These problems were taken on the AOPS website.

", "hints_md": "", "hints_html": "", "editorial_md": "", "editorial_html": "", "flag_hint": "", "point_value": 6, "problem_name": "1991 AIME Problem 15", "can_next": false, "can_prev": true, "nxt": "", "prev": "/problem/91_aime_p14"}}