{"status": "success", "data": {"description_md": "The Cotsworth calendar (also called the \"International Fixed Calendar\") is a calendar system in which every month has $28$ days except for $1$ month which has $29$ days (there are $13$ months total). However, in the world of Sbrtugimmurstyj, December $31^\\text{st}$ does **not** exist (Sbrtugimmurstyjies hate the New Year), so January $1^\\text{st}$ is **always** a Sunday (this means there are $13$ months of $28$ days each). In this world, there exists some number of people. What is the minimum number of people needed to exist such that in any month of a year, there exists one week containing at least $3$ people's birthdays?", "description_html": "<p>The Cotsworth calendar (also called the &#8220;International Fixed Calendar&#8221;) is a calendar system in which every month has <span class=\"katex--inline\">28</span> days except for <span class=\"katex--inline\">1</span> month which has <span class=\"katex--inline\">29</span> days (there are <span class=\"katex--inline\">13</span> months total). However, in the world of Sbrtugimmurstyj, December <span class=\"katex--inline\">31^\\text{st}</span> does <strong>not</strong> exist (Sbrtugimmurstyjies hate the New Year), so January <span class=\"katex--inline\">1^\\text{st}</span> is <strong>always</strong> a Sunday (this means there are <span class=\"katex--inline\">13</span> months of <span class=\"katex--inline\">28</span> days each). In this world, there exists some number of people. What is the minimum number of people needed to exist such that in any month of a year, there exists one week containing at least <span class=\"katex--inline\">3</span> people&#8217;s birthdays?</p>&#10;", "hints_md": "", "hints_html": "", "editorial_md": "", "editorial_html": "", "flag_hint": "", "point_value": 1, "problem_name": "Holiday Contest 2025 - Guts Round - Set 1 Problem 1", "can_next": false, "can_prev": false, "nxt": "", "prev": ""}}