{"status": "success", "data": {"description_md": "Let there be $2$ identical unfair $10$-sided die with sides labeled $1-10$. $P$ denotes the probability that the $2$ die roll equal values. If $\\min(P)$ can be denoted by $\\frac{m}{n}$, where $m$ and $n$ are both relatively prime, positive integers, compute $10m + n$.", "description_html": "<p>Let there be <span class=\"katex--inline\">2</span> identical unfair <span class=\"katex--inline\">10</span>-sided die with sides labeled <span class=\"katex--inline\">1-10</span>. <span class=\"katex--inline\">P</span> denotes the probability that the <span class=\"katex--inline\">2</span> die roll equal values. If <span class=\"katex--inline\">\\min(P)</span> can be denoted by <span class=\"katex--inline\">\\frac{m}{n}</span>, where <span class=\"katex--inline\">m</span> and <span class=\"katex--inline\">n</span> are both relatively prime, positive integers, compute <span class=\"katex--inline\">10m + n</span>.</p>&#10;", "hints_md": "", "hints_html": "", "editorial_md": "", "editorial_html": "", "flag_hint": "", "point_value": 4, "problem_name": "March Break 2024 - Problem 1", "can_next": false, "can_prev": false, "nxt": "", "prev": ""}}