{"status": "success", "data": {"description_md": "**POTD March 30, 2024**\n\nA parking lot consists of $2012$ parking spots equally spaced in a line, numbered $1$ through $2012.$ One by one, $2012$ cars park in these spots under the following procedure: the first car picks from the $2012$ spots uniformly randomly, and each following car picks uniformly randomly among all possible choices which maximize the minimal distance from an already parked car.\n\nIf the probability that the last car to park must choose spot $1$ can be written as $\\frac{m}{n}$, where $m$ and $n$ are relatively prime positive integers, find $m+n$.", "description_html": "<p><strong>POTD March 30, 2024</strong></p>&#10;<p>A parking lot consists of <span class=\"katex--inline\">2012</span> parking spots equally spaced in a line, numbered <span class=\"katex--inline\">1</span> through <span class=\"katex--inline\">2012.</span> One by one, <span class=\"katex--inline\">2012</span> cars park in these spots under the following procedure: the first car picks from the <span class=\"katex--inline\">2012</span> spots uniformly randomly, and each following car picks uniformly randomly among all possible choices which maximize the minimal distance from an already parked car.</p>&#10;<p>If the probability that the last car to park must choose spot <span class=\"katex--inline\">1</span> can be written 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": 6, "problem_name": "Problem of the Day #112", "can_next": false, "can_prev": false, "nxt": "", "prev": ""}}