{"status": "success", "data": {"description_md": "Let $a, b, c, d$ be non-negative reals such that $a + b + c + d = 12$. If the sum of the maximum and the minimum value of $${a + 1} + \\sqrt{2b + 1} + \\sqrt{3c + 1} + \\sqrt{6d + 1} $$\n    \ncan be expressed as $p + \\sqrt{q} + r\\sqrt{s}$, where $p$, $q$, $r$, and $s$ are positive integers, and $q$ and $s$ are not divisible by the square of any prime,    compute $p + q + r + s$.  ", "description_html": "<p>Let <span class=\"katex--inline\">a, b, c, d</span> be non-negative reals such that <span class=\"katex--inline\">a + b + c + d = 12</span>. If the sum of the maximum and the minimum value of <span class=\"katex--display\">{a + 1} + \\sqrt{2b + 1} + \\sqrt{3c + 1} + \\sqrt{6d + 1}</span></p>&#10;<p>can be expressed as <span class=\"katex--inline\">p + \\sqrt{q} + r\\sqrt{s}</span>, where <span class=\"katex--inline\">p</span>, <span class=\"katex--inline\">q</span>, <span class=\"katex--inline\">r</span>, and <span class=\"katex--inline\">s</span> are positive integers, and <span class=\"katex--inline\">q</span> and <span class=\"katex--inline\">s</span> are not divisible by the square of any prime,    compute <span class=\"katex--inline\">p + q + r + s</span>.</p>&#10;", "hints_md": "", "hints_html": "", "editorial_md": "", "editorial_html": "", "flag_hint": "", "point_value": 4, "problem_name": "TxO Math Bowl 2024 - Team Contest - Problem 13", "can_next": true, "can_prev": true, "nxt": "/problem/txo2024team-p14", "prev": "/problem/txo2024team-p12"}}