{"status": "success", "data": {"description_md": "Consider a sphere tangent to four faces of a unit octahedron that share a vertex. Suppose this sphere passes through the opposite vertex. If the radius of this sphere can be expressed as $\\frac{\\sqrt{a}-\\sqrt{b}}{c}$, where $a$, $b$, and $c$ are positive integers, and $a$, $b$ are not divisible by the square of any prime, find $100a+10b+c$.", "description_html": "<p>Consider a sphere tangent to four faces of a unit octahedron that share a vertex. Suppose this sphere passes through the opposite vertex. If the radius of this sphere can be expressed as <span class=\"katex--inline\">\\frac{\\sqrt{a}-\\sqrt{b}}{c}</span>, where <span class=\"katex--inline\">a</span>, <span class=\"katex--inline\">b</span>, and <span class=\"katex--inline\">c</span> are positive integers, and <span class=\"katex--inline\">a</span>, <span class=\"katex--inline\">b</span> are not divisible by the square of any prime, find <span class=\"katex--inline\">100a+10b+c</span>.</p>&#10;", "hints_md": "", "hints_html": "", "editorial_md": "", "editorial_html": "", "flag_hint": "", "point_value": 5, "problem_name": "March Break 2024 - Problem 8", "can_next": false, "can_prev": false, "nxt": "", "prev": ""}}