{"status": "success", "data": {"description_md": "There are $2024$ people standing in a line. Each person picks a random real number between $0$ and $1$. A person, not on either endpoint, is called a *mountain* if their number is bigger than both their neighbors' numbers. Find the expected value of the number of mountains.", "description_html": "<p>There are <span class=\"katex--inline\">2024</span> people standing in a line. Each person picks a random real number between <span class=\"katex--inline\">0</span> and <span class=\"katex--inline\">1</span>. A person, not on either endpoint, is called a <em>mountain</em> if their number is bigger than both their neighbors&#8217; numbers. Find the expected value of the number of mountains.</p>&#10;", "hints_md": "", "hints_html": "", "editorial_md": "", "editorial_html": "", "flag_hint": "", "point_value": 3, "problem_name": "Holiday Contest 2025 - Individual Round - Problem 4", "can_next": false, "can_prev": false, "nxt": "", "prev": ""}}