{"status": "success", "data": {"description_md": "**POTD June 19, 2024**\n\nAva and Tiffany participate in a knockout tournament consisting of a total of $32$ players. In each of $5$ rounds, the remaining players are paired uniformly at random. In each pair, both players are equally likely to win, and the loser is knocked out of the tournament. The probability that Ava and Tiffany play each other during the tournament is $\\frac{a}{b}$, where $a$ and $b$ are relatively prime positive integers. Compute $100a + b$.", "description_html": "<p><strong>POTD June 19, 2024</strong></p>&#10;<p>Ava and Tiffany participate in a knockout tournament consisting of a total of <span class=\"katex--inline\">32</span> players. In each of <span class=\"katex--inline\">5</span> rounds, the remaining players are paired uniformly at random. In each pair, both players are equally likely to win, and the loser is knocked out of the tournament. The probability that Ava and Tiffany play each other during the tournament is <span class=\"katex--inline\">\\frac{a}{b}</span>, where <span class=\"katex--inline\">a</span> and <span class=\"katex--inline\">b</span> are relatively prime positive integers. Compute <span class=\"katex--inline\">100a + b</span>.</p>&#10;", "hints_md": "", "hints_html": "", "editorial_md": "", "editorial_html": "", "flag_hint": "", "point_value": 3, "problem_name": "Problem of the Day #192", "can_next": false, "can_prev": false, "nxt": "", "prev": ""}}