Question 24
On planet Alpha they use an alphabet of $100$ letters. A word is a sequence of letters that satisfies the following conditions:
*No two consecutive letters are the same. For example, BEAUTY is not a word, because it has LL, and COOPERATE is not a word because it has OO.
* There are no two different letters $U$ and $V$ that appear in the order $UVUV$, not even if other letters are interspersed between each two of them. For example, ANSWER is not a word because it has ESES, and FIFTY is not a word because it has CNCN.
Determine the maximum length that a word can have.
*No two consecutive letters are the same. For example, BEAUTY is not a word, because it has LL, and COOPERATE is not a word because it has OO.
* There are no two different letters $U$ and $V$ that appear in the order $UVUV$, not even if other letters are interspersed between each two of them. For example, ANSWER is not a word because it has ESES, and FIFTY is not a word because it has CNCN.
Determine the maximum length that a word can have.