{"status": "success", "data": {"description_md": "A spinner wheel is split into three sectors, each labeled with positive integers $a$, $b$, and $c$. The number on each sector is proportional to the probability the sector gets landed on when the wheel is spun. For example, a sector labeled with $6$ is three times as likely to be landed on than a sector labeled with $2$. When the wheel is spun, the expected value of the label of the sector the wheel lands on is $7$. Compute the sum of all possible values of $a+b+c$.", "description_html": "<p>A spinner wheel is split into three sectors, each labeled with positive integers <span class=\"katex--inline\">a</span>, <span class=\"katex--inline\">b</span>, and <span class=\"katex--inline\">c</span>. The number on each sector is proportional to the probability the sector gets landed on when the wheel is spun. For example, a sector labeled with <span class=\"katex--inline\">6</span> is three times as likely to be landed on than a sector labeled with <span class=\"katex--inline\">2</span>. When the wheel is spun, the expected value of the label of the sector the wheel lands on is <span class=\"katex--inline\">7</span>. Compute the sum of all possible values of <span class=\"katex--inline\">a+b+c</span>.</p>&#10;", "hints_md": "", "hints_html": "", "editorial_md": "", "editorial_html": "", "flag_hint": "", "point_value": 4, "problem_name": "Holiday Contest 2025 - Individual Round - Problem 6", "can_next": false, "can_prev": false, "nxt": "", "prev": ""}}