{"status": "success", "data": {"description_md": "**POTD November 29, 2023**\n**Author:** munch\n\nIf we draw a regular octagon and all of its diagonals, we find that inside the octagon, there are eight points where exactly $3$ diagonals concur, and one point where exactly four diagonals concur. The diagonals divide the octagon into $80$ distinct regions. If we do the same for a regular $12$-gon, we find that inside the $12$-gon, there are $60$ points where exactly three diagonals concur, $12$ points where exactly four diagonals concur, and one point where exactly six diagonals concur. These are all the points inside the $12$-gon where at least three diagonals concur. How many distinct regions are there in the $12$-gon?", "description_html": "<p><strong>POTD November 29, 2023</strong><br/>&#10;<strong>Author:</strong> munch</p>&#10;<p>If we draw a regular octagon and all of its diagonals, we find that inside the octagon, there are eight points where exactly <span class=\"katex--inline\">3</span> diagonals concur, and one point where exactly four diagonals concur. The diagonals divide the octagon into <span class=\"katex--inline\">80</span> distinct regions. If we do the same for a regular <span class=\"katex--inline\">12</span>-gon, we find that inside the <span class=\"katex--inline\">12</span>-gon, there are <span class=\"katex--inline\">60</span> points where exactly three diagonals concur, <span class=\"katex--inline\">12</span> points where exactly four diagonals concur, and one point where exactly six diagonals concur. These are all the points inside the <span class=\"katex--inline\">12</span>-gon where at least three diagonals concur. How many distinct regions are there in the <span class=\"katex--inline\">12</span>-gon?</p>&#10;", "hints_md": "", "hints_html": "", "editorial_md": "", "editorial_html": "", "flag_hint": "", "point_value": 4, "problem_name": "Problem of the Day #10", "can_next": false, "can_prev": false, "nxt": "", "prev": ""}}