{"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 <span class=\"katex--inline\">(5,0)</span>. Define a move for the particle as a counterclockwise rotation of <span class=\"katex--inline\">\\pi/4</span> radians about the origin followed by a translation of <span class=\"katex--inline\">10</span> units in the positive <span class=\"katex--inline\">x</span>-direction. Given that the particle&#8217;s position after <span class=\"katex--inline\">150</span> moves is <span class=\"katex--inline\">(p,q)</span>, find the greatest integer less than or equal to <span class=\"katex--inline\">|p|+|q|</span>.</p>&#10;<hr/>&#10;<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>&#10;", "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"}}