{"status": "success", "data": {"description_md": "A particle is located on the coordinate plane at $ (5,0)$. Define a move for the particle as a counterclockwise rotation of $ \\pi/4$ radians about the origin followed by a translation of $ 10$ units in the positive $ x$-direction. Given that the particle's position after $ 150$ moves is $ (p,q)$, find the greatest integer less than or equal to $ |p|+|q|$.\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>A particle is located on the coordinate plane at $ (5,0)$. Define a move for the particle as a counterclockwise rotation of $ \\pi/4$ radians about the origin followed by a translation of $ 10$ units in the positive $ x$-direction. Given that the particle&#8217;s position after $ 150$ moves is $ (p,q)$, find the greatest integer less than or equal to $ |p|+|q|$.</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": 4, "problem_name": "2008 AIME II Problem 9", "can_next": true, "can_prev": true, "nxt": "/problem/08_aime_II_p10", "prev": "/problem/08_aime_II_p08"}}