{"status": "success", "data": {"description_md": "Consider sequences that consist entirely of $A$'s and $B$'s and that have the property that every run of consecutive $A$'s has even length, and every run of consecutive $B$'s has odd length. Examples of such sequences are $AA$, $B$, and $AABAA$, while $BBAB$ is not such a sequence. How many such sequences have length $14$?\n___\nLeading zeroes must be inputted, so if your answer is `34`, then input `034`. Full credit goes to [MAA](https://maa.org/) for authoring these problems. These problems were taken on the [AOPS](https://artofproblemsolving.com/) website.", "description_html": "<p>Consider sequences that consist entirely of <span class=\"katex--inline\">A</span>'s and <span class=\"katex--inline\">B</span>'s and that have the property that every run of consecutive <span class=\"katex--inline\">A</span>'s has even length, and every run of consecutive <span class=\"katex--inline\">B</span>'s has odd length. Examples of such sequences are <span class=\"katex--inline\">AA</span>, <span class=\"katex--inline\">B</span>, and <span class=\"katex--inline\">AABAA</span>, while <span class=\"katex--inline\">BBAB</span> is not such a sequence. How many such sequences have length <span class=\"katex--inline\">14</span>?</p>&#10;<hr/>&#10;<p>Leading zeroes must be inputted, so if your answer is <code>34</code>, then input <code>034</code>. Full credit goes to <a href=\"https://maa.org/\">MAA</a> for authoring these problems. These problems were taken on the <a href=\"https://artofproblemsolving.com/\">AOPS</a> website.</p>&#10;", "hints_md": "", "hints_html": "", "editorial_md": "", "editorial_html": "", "flag_hint": "", "point_value": 5, "problem_name": "2008 AIME I Problem 11", "can_next": true, "can_prev": true, "nxt": "/problem/08_aime_I_p12", "prev": "/problem/08_aime_I_p10"}}