{"status": "success", "data": {"description_md": "Let $N$ be the number of strings (words) of length $7$ such that each character is in the set $\\{A,B,C,D\\}$, and that given any four consecutive characters from the string, they are not all distinct. Find the remainder when $N$ is divided by $100$.\n\nFor example, $ABCBBDA$ is valid, as out of $ABCB$, $BCBB$, $CBBD$, and $BBDA$, each of them contain at least one duplicate letter, but $ABCDABB$ is invalid, because the letters in $BCDA$ are all distinct", "description_html": "<p>Let <span class=\"katex--inline\">N</span> be the number of strings (words) of length <span class=\"katex--inline\">7</span> such that each character is in the set <span class=\"katex--inline\">\\{A,B,C,D\\}</span>, and that given any four consecutive characters from the string, they are not all distinct. Find the remainder when <span class=\"katex--inline\">N</span> is divided by <span class=\"katex--inline\">100</span>.</p>&#10;<p>For example, <span class=\"katex--inline\">ABCBBDA</span> is valid, as out of <span class=\"katex--inline\">ABCB</span>, <span class=\"katex--inline\">BCBB</span>, <span class=\"katex--inline\">CBBD</span>, and <span class=\"katex--inline\">BBDA</span>, each of them contain at least one duplicate letter, but <span class=\"katex--inline\">ABCDABB</span> is invalid, because the letters in <span class=\"katex--inline\">BCDA</span> are all distinct</p>&#10;", "hints_md": "", "hints_html": "", "editorial_md": "", "editorial_html": "", "flag_hint": "", "point_value": 6, "problem_name": "TxO Math Bowl 2024 - Individuals A - Problem 14", "can_next": true, "can_prev": true, "nxt": "/problem/txo2024indivsA-p15", "prev": "/problem/txo2024indivsA-p13"}}