{"status": "success", "data": {"description_md": "A cookie is given to one of eight children sitting equidistantly along a round table. Each turn, the child with the cookie hands it to either a neighbor or the child diametrically opposite of them, chosen uniformly at random. Alice and Bob are sitting such that there is one person sitting between them. If Alice starts with a cookie, the expected value of the number of turns until Bob gets handed the cookie can be written as $a/b$ where $a$ and $b$ are relatively prime positive integers. Find $a + b$.", "description_html": "<p>A cookie is given to one of eight children sitting equidistantly along a round table. Each turn, the child with the cookie hands it to either a neighbor or the child diametrically opposite of them, chosen uniformly at random. Alice and Bob are sitting such that there is one person sitting between them. If Alice starts with a cookie, the expected value of the number of turns until Bob gets handed the cookie can be written as <span class=\"katex--inline\">a/b</span> where <span class=\"katex--inline\">a</span> and <span class=\"katex--inline\">b</span> are relatively prime positive integers. Find <span class=\"katex--inline\">a + b</span>.</p>&#10;", "hints_md": "", "hints_html": "", "editorial_md": "", "editorial_html": "", "flag_hint": "", "point_value": 4, "problem_name": "Grinding Aces Math Exam 2025 - Problem 4", "can_next": false, "can_prev": false, "nxt": "", "prev": ""}}