{"status": "success", "data": {"description_md": "The sum of the following seven numbers is exactly 19:
\n$$a_1=2.56,\\qquad a_2=2.61,\\qquad a_3=2.65,\\qquad a_4=2.71, $$$$a_5=2.79,\\qquad a_6=2.82,\\qquad a_7=2.86. $$It is desired to replace each $a_i$ by an integer approximation $A_i$, $1 \\le i \\le 7$, so that the sum of the $A_i$'s is also 19 and so that $M$, the maximum of the \"errors\" $|A_i - a_i|$, is as small as possible. For this minimum $M$, what is $100M$?\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": "

The sum of the following seven numbers is exactly 19:
a_1=2.56,\\qquad a_2=2.61,\\qquad a_3=2.65,\\qquad a_4=2.71,a_5=2.79,\\qquad a_6=2.82,\\qquad a_7=2.86.It is desired to replace each a_i by an integer approximation A_i, 1 \\le i \\le 7, so that the sum of the A_i's is also 19 and so that M, the maximum of the “errors” |A_i - a_i|, is as small as possible. For this minimum M, what is 100M?

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": 4, "problem_name": "1985 AIME Problem 8", "can_next": true, "can_prev": true, "nxt": "/problem/85_aime_p09", "prev": "/problem/85_aime_p07"}}