{"status": "success", "data": {"description_md": "Call an integer $a$ bad if there exists another integer $b$ such that $a \\equiv b^2 \\pmod{44}$. Numbers are randomly drawn from $\\{1,2,\\ldots,2024\\}$ (without replacement) until a bad number is drawn. Say we draw $K$ cards. If the expected value of $K$ can be written as $\\frac{a}{b}$, where $a$ and $b$ are relatively prime positive integers, find $a+b$.", "description_html": "<p>Call an integer <span class=\"katex--inline\">a</span> bad if there exists another integer <span class=\"katex--inline\">b</span> such that <span class=\"katex--inline\">a \\equiv b^2 \\pmod{44}</span>. Numbers are randomly drawn from <span class=\"katex--inline\">\\{1,2,\\ldots,2024\\}</span> (without replacement) until a bad number is drawn. Say we draw <span class=\"katex--inline\">K</span> cards. If the expected value of <span class=\"katex--inline\">K</span> can be written as <span class=\"katex--inline\">\\frac{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": 7, "problem_name": "Holiday Contest 2025 - Guts Round - Set 8 Problem 2", "can_next": false, "can_prev": false, "nxt": "", "prev": ""}}