{"status": "success", "data": {"description_md": "Let $ S$ be the set of points in the Cartesian plane that satisfy<br>\n$$ \\Big|\\big|{|x| - 2}\\big| - 1\\Big| + \\Big|\\big|{|y| - 2}\\big| - 1\\Big| = 1.<br>\n$$ If a model of $ S$ were built from wire of negligible thickness, then the total length of wire required would be $ a\\sqrt {b},$ where $ a$ and $ b$ are positive integers and $ b$ is not divisible by the square of any prime number. Find $ a + b.$\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": "<p>Let $ S$ be the set of points in the Cartesian plane that satisfy<br/><span class=\"katex--display\"> \\Big|\\big|{|x| - 2}\\big| - 1\\Big| + \\Big|\\big|{|y| - 2}\\big| - 1\\Big| = 1.&lt;br&gt;</span><br/>If a model of $ S$ were built from wire of negligible thickness, then the total length of wire required would be $ a\\sqrt {b},$ where $ a$ and $ b$ are positive integers and $ b$ is not divisible by the square of any prime number. Find $ a + b.$</p>&#10;<hr><p>Leading zeroes must be inputted, so if your answer is <code>34</code>, then input <code>034</code>. Full credit goes to <a href=\"https://maa.org/\">MAA</a> for authoring these problems. These problems were taken on the <a href=\"https://artofproblemsolving.com/\">AOPS</a> website.</p>", "hints_md": "", "hints_html": "", "editorial_md": "", "editorial_html": "", "flag_hint": "", "point_value": 6, "problem_name": "1997 AIME Problem 13", "can_next": true, "can_prev": true, "nxt": "/problem/97_aime_p14", "prev": "/problem/97_aime_p12"}}