{"status": "success", "data": {"description_md": "**POTD May 31, 2024**\n\nCount the number of functions $f : \\mathbb{Z} \\rightarrow \\{\\text{\u2018green\u2019, \u2018blue\u2019}\\}$ such that $f(x) = f(x + 22)$ for all integers $x$ and there does not exist an integer $y$ with $f(y) = f(y + 2) = \\text{\u2018green\u2019}$.", "description_html": "<p><strong>POTD May 31, 2024</strong></p>&#10;<p>Count the number of functions <span class=\"katex--inline\">f : \\mathbb{Z} \\rightarrow \\{\\text{&#8216;green&#8217;, &#8216;blue&#8217;}\\}</span> such that <span class=\"katex--inline\">f(x) = f(x + 22)</span> for all integers <span class=\"katex--inline\">x</span> and there does not exist an integer <span class=\"katex--inline\">y</span> with <span class=\"katex--inline\">f(y) = f(y + 2) = \\text{&#8216;green&#8217;}</span>.</p>&#10;", "hints_md": "", "hints_html": "", "editorial_md": "", "editorial_html": "", "flag_hint": "", "point_value": 5, "problem_name": "Problem of the Day #173", "can_next": false, "can_prev": false, "nxt": "", "prev": ""}}