{"status": "success", "data": {"description_md": "**POTD April 4, 2024**\n\nLet $N$ be the number of ordered pairs of nonempty sets $\\mathbb{A}$ and $\\mathbb{B}$ that have the following properties:\n\n$\\mathbb{A} \\cup \\mathbb{B} = \\{1,2,3,4,5,6,7,8,9,10,11,12\\}$,\n$\\mathbb{A} \\cap \\mathbb{B} = \\emptyset$,\nThe number of elements of $\\mathbb{A}$ is not an element of $\\mathbb{A}$,\nThe number of elements of $\\mathbb{B}$ is not an element of $\\mathbb{B}$.", "description_html": "<p><strong>POTD April 4, 2024</strong></p>&#10;<p>Let <span class=\"katex--inline\">N</span> be the number of ordered pairs of nonempty sets <span class=\"katex--inline\">\\mathbb{A}</span> and <span class=\"katex--inline\">\\mathbb{B}</span> that have the following properties:</p>&#10;<p><span class=\"katex--inline\">\\mathbb{A} \\cup \\mathbb{B} = \\{1,2,3,4,5,6,7,8,9,10,11,12\\}</span>,<br/>&#10;<span class=\"katex--inline\">\\mathbb{A} \\cap \\mathbb{B} = \\emptyset</span>,<br/>&#10;The number of elements of <span class=\"katex--inline\">\\mathbb{A}</span> is not an element of <span class=\"katex--inline\">\\mathbb{A}</span>,<br/>&#10;The number of elements of <span class=\"katex--inline\">\\mathbb{B}</span> is not an element of <span class=\"katex--inline\">\\mathbb{B}</span>.</p>&#10;", "hints_md": "", "hints_html": "", "editorial_md": "", "editorial_html": "", "flag_hint": "", "point_value": 3, "problem_name": "Problem of the Day #117", "can_next": false, "can_prev": false, "nxt": "", "prev": ""}}