{"status": "success", "data": {"description_md": "Consider the L-shaped region formed by three unit squares joined at their sides, as shown below. Two points $A$ and $B$ are chosen independently and uniformly at random from inside this region. The probability that the midpoint of $\\overline{AB}$ also lies inside this L-shaped region can be expressed as $\\frac{m}{n}$, where $m$ and $n$ are relatively prime positive integers. Find $m+n$.
$\\includegraphics[width=59, height=59, totalheight=59]{https://latex.artofproblemsolving.com/d/a/b/dab5e4a4438a66a5365a97b107e467ca2403c36f.png}$\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": "

Consider the L-shaped region formed by three unit squares joined at their sides, as shown below. Two points A and B are chosen independently and uniformly at random from inside this region. The probability that the midpoint of \\overline{AB} also lies inside this L-shaped region can be expressed as \\frac{m}{n}, 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": 4, "problem_name": "2023 AIME II Problem 6", "can_next": true, "can_prev": true, "nxt": "/problem/23_aime_II_p07", "prev": "/problem/23_aime_II_p05"}}