{"status": "success", "data": {"description_md": "**POTD April 18, 2024**\n\nConsider a set $\\mathcal{A}$ with $10$ distinct positive integer elements such that for every $\\mathcal{S} \\subseteq \\mathcal{A}$ with $|\\mathcal{S}| > 0$, where $|\\mathcal{S}|$ denotes the cardinality of set $\\mathcal{S}$, the sum of elements in $\\mathcal{S}$ is divisible by $|\\mathcal{S}|$. Find the minimum possible value of the sum of elements in $\\mathcal{A}$.", "description_html": "<p><strong>POTD April 18, 2024</strong></p>&#10;<p>Consider a set <span class=\"katex--inline\">\\mathcal{A}</span> with <span class=\"katex--inline\">10</span> distinct positive integer elements such that for every <span class=\"katex--inline\">\\mathcal{S} \\subseteq \\mathcal{A}</span> with <span class=\"katex--inline\">|\\mathcal{S}| &gt; 0</span>, where <span class=\"katex--inline\">|\\mathcal{S}|</span> denotes the cardinality of set <span class=\"katex--inline\">\\mathcal{S}</span>, the sum of elements in <span class=\"katex--inline\">\\mathcal{S}</span> is divisible by <span class=\"katex--inline\">|\\mathcal{S}|</span>. Find the minimum possible value of the sum of elements in <span class=\"katex--inline\">\\mathcal{A}</span>.</p>&#10;", "hints_md": "", "hints_html": "", "editorial_md": "", "editorial_html": "", "flag_hint": "", "point_value": 4, "problem_name": "Problem of the Day #130", "can_next": false, "can_prev": false, "nxt": "", "prev": ""}}