{"status": "success", "data": {"description_md": "Three numbers, $a_1$, $a_2$, $a_3$, are drawn randomly and without replacement from the set $\\{1, 2, 3, \\ldots, 1000\\}$. Three other numbers, $b_1$, $b_2$, $b_3$, are then drawn randomly and without replacement from the remaining set of 997 numbers. Let $p$ be the probability that, after a suitable rotation, a brick of dimensions $a_1 \\times a_2 \\times a_3$ can be enclosed in a box of dimensions $b_1 \\times b_2 \\times b_3$, with the sides of the brick parallel to the sides of the box. If $p$ is written as a fraction in lowest terms, what is the sum of the numerator and denominator?\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": "

Three numbers, a_1, a_2, a_3, are drawn randomly and without replacement from the set \\{1, 2, 3, \\ldots, 1000\\}. Three other numbers, b_1, b_2, b_3, are then drawn randomly and without replacement from the remaining set of 997 numbers. Let p be the probability that, after a suitable rotation, a brick of dimensions a_1 \\times a_2 \\times a_3 can be enclosed in a box of dimensions b_1 \\times b_2 \\times b_3, with the sides of the brick parallel to the sides of the box. If p is written as a fraction in lowest terms, what is the sum of the numerator and denominator?

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": "1993 AIME Problem 7", "can_next": true, "can_prev": true, "nxt": "/problem/93_aime_p08", "prev": "/problem/93_aime_p06"}}