{"status": "success", "data": {"description_md": "A positive $3-$digit base ten integer is chosen randomly. The probability that this base-$10$ string is not valid in base $7$ (For example the string $547_7$ is invalid) can be expressed as $\\frac{a}{b}$, where $a$ and $b$ are relatively prime positive integers. Compute $a+b$.", "description_html": "<p>A positive <span class=\"katex--inline\">3-</span>digit base ten integer is chosen randomly. The probability that this base-<span class=\"katex--inline\">10</span> string is not valid in base <span class=\"katex--inline\">7</span> (For example the string <span class=\"katex--inline\">547_7</span> is invalid) can be expressed 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. Compute <span class=\"katex--inline\">a+b</span>.</p>&#10;", "hints_md": "", "hints_html": "", "editorial_md": "", "editorial_html": "", "flag_hint": "", "point_value": 2, "problem_name": "TxO Math Bowl 2024 - Team Contest - Problem 2", "can_next": true, "can_prev": true, "nxt": "/problem/txo2024team-p03", "prev": "/problem/txo2024team-p01"}}