{"status": "success", "data": {"description_md": "A cat walks from $(0, 0)$ to $(11, 7)$ on the coordinate plane in $20$ steps. On each step, the cat walks one unit in the positive or negative, $x$ or $y$ direction (so it can walk in all 4 cardinal directions). Let $m$ be the number of possible paths that the cat could take if it cannot turn $180^\\circ$ while changing direction. Compute the number of positive factors of $m$.", "description_html": "<p>A cat walks from <span class=\"katex--inline\">(0, 0)</span> to <span class=\"katex--inline\">(11, 7)</span> on the coordinate plane in <span class=\"katex--inline\">20</span> steps. On each step, the cat walks one unit in the positive or negative, <span class=\"katex--inline\">x</span> or <span class=\"katex--inline\">y</span> direction (so it can walk in all 4 cardinal directions). Let <span class=\"katex--inline\">m</span> be the number of possible paths that the cat could take if it cannot turn <span class=\"katex--inline\">180^\\circ</span> while changing direction. Compute the number of positive factors of <span class=\"katex--inline\">m</span>.</p>&#10;", "hints_md": "", "hints_html": "", "editorial_md": "", "editorial_html": "", "flag_hint": "", "point_value": 4, "problem_name": "TxO Math Bowl 2024 - Guts Contest - Set 4 Problem 1", "can_next": false, "can_prev": false, "nxt": "", "prev": ""}}