{"status": "success", "data": {"description_md": "How many non-empty subsets $\\mathcal{S}$ of $\\{1,2,3,4,5,6,7,8,9\\}$ are there such that no element of $\\mathcal{S}$ is relatively prime to all other elements in $\\mathcal{S}$?\n\nNote: one element sets do not satisfy these conditions.", "description_html": "<p>How many non-empty subsets <span class=\"katex--inline\">\\mathcal{S}</span> of <span class=\"katex--inline\">\\{1,2,3,4,5,6,7,8,9\\}</span> are there such that no element of <span class=\"katex--inline\">\\mathcal{S}</span> is relatively prime to all other elements in <span class=\"katex--inline\">\\mathcal{S}</span>?</p>&#10;<p>Note: one element sets do not satisfy these conditions.</p>&#10;", "hints_md": "", "hints_html": "", "editorial_md": "", "editorial_html": "", "flag_hint": "", "point_value": 4, "problem_name": "TxO Math Bowl 2024 - Team Contest - Problem 11", "can_next": true, "can_prev": true, "nxt": "/problem/txo2024team-p12", "prev": "/problem/txo2024team-p10"}}