{"status": "success", "data": {"description_md": "A sequence of numbers $x_{1},x_{2},x_{3},\\ldots,x_{100}$ has the property that, for every integer $k$ between $1$ and $100,$ inclusive, the number $x_{k}$ is $k$ less than the sum of the other $99$ numbers. Given that $x_{50}=\\frac mn,$ where $m$ and $n$ are relatively prime positive integers, find $m+n.$\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": "

A sequence of numbers x_{1},x_{2},x_{3},\\ldots,x_{100} has the property that, for every integer k between 1 and 100, inclusive, the number x_{k} is k less than the sum of the other 99 numbers. Given that x_{50}=\\frac mn, where m and n are relatively prime positive integers, find m+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": 5, "problem_name": "2000 AIME I Problem 10", "can_next": true, "can_prev": true, "nxt": "/problem/00_aime_I_p11", "prev": "/problem/00_aime_I_p09"}}