{"status": "success", "data": {"description_md": "**POTD January 9, 2024**\n*Note that POTD structure was changed again to have a random point difficulty every day*\n**Author:** awesomeming327\n\nThree nonoverlapping regular hexagons share a vertex. Max stands at a random point on the same plane. The expected value of the number of hexagon vertices he can see (if two hexagons have a vertex in common, that vertex counts as one vertex rather than two) can be expressed as $\\frac{m}{n}$ where $m$ and $n$ are relatively prime positive integers. Find $m + n$.", "description_html": "<p><strong>POTD January 9, 2024</strong><br/>&#10;<em>Note that POTD structure was changed again to have a random point difficulty every day</em><br/>&#10;<strong>Author:</strong> awesomeming327</p>&#10;<p>Three nonoverlapping regular hexagons share a vertex. Max stands at a random point on the same plane. The expected value of the number of hexagon vertices he can see (if two hexagons have a vertex in common, that vertex counts as one vertex rather than two) can be expressed as <span class=\"katex--inline\">\\frac{m}{n}</span> where <span class=\"katex--inline\">m</span> and <span class=\"katex--inline\">n</span> are relatively prime positive integers. Find <span class=\"katex--inline\">m + n</span>.</p>&#10;", "hints_md": "", "hints_html": "", "editorial_md": "", "editorial_html": "", "flag_hint": "", "point_value": 3, "problem_name": "Problem of the Day #35", "can_next": false, "can_prev": false, "nxt": "", "prev": ""}}