{"status": "success", "data": {"description_md": "A piece of chalk has a durability of $40$ units. It takes $1$ unit of durability to draw the letter $A$ and $2$ units of durability to draw the letter $B$. A sequence of $A$'s and $B$'s is made where no $A$ can appear more than $2$ times in a row and no $B$ can appear more than $1$ time in a row. How many different sequences of exactly length $30$ can be drawn with one piece of chalk?", "description_html": "<p>A piece of chalk has a durability of <span class=\"katex--inline\">40</span> units. It takes <span class=\"katex--inline\">1</span> unit of durability to draw the letter <span class=\"katex--inline\">A</span> and <span class=\"katex--inline\">2</span> units of durability to draw the letter <span class=\"katex--inline\">B</span>. A sequence of <span class=\"katex--inline\">A</span>'s and <span class=\"katex--inline\">B</span>'s is made where no <span class=\"katex--inline\">A</span> can appear more than <span class=\"katex--inline\">2</span> times in a row and no <span class=\"katex--inline\">B</span> can appear more than <span class=\"katex--inline\">1</span> time in a row. How many different sequences of exactly length <span class=\"katex--inline\">30</span> can be drawn with one piece of chalk?</p>&#10;", "hints_md": "", "hints_html": "", "editorial_md": "", "editorial_html": "", "flag_hint": "", "point_value": 5, "problem_name": "Holiday Contest 2025 - Guts Round - Set 7 Problem 2", "can_next": false, "can_prev": false, "nxt": "", "prev": ""}}