{"status": "success", "data": {"description_md": "Each vertex of a regular octagon is coloured either red or blue with equal probability. The probability that the octagon can then be rotated in such a way that all of the blue vertices end up at points that were originally red is $\\tfrac{m}{n}$, where $m$ and $n$ are relatively prime positive integers. What is $m+n$?\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>Each vertex of a regular octagon is coloured either red or blue with equal probability. The probability that the octagon can then be rotated in such a way that all of the blue vertices end up at points that were originally red is <span class=\"katex--inline\">\\tfrac{m}{n}</span>, where <span class=\"katex--inline\">m</span> and <span class=\"katex--inline\">n</span> are relatively prime positive integers. What is <span class=\"katex--inline\">m+n</span>?</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": 5, "problem_name": "2024 AIME I Problem 11", "can_next": true, "can_prev": true, "nxt": "/problem/24_aime_I_p12", "prev": "/problem/24_aime_I_p10"}}