Question 2
On Babba Island they use a two-letter alphabet, $a$ and $b$, and every (finite) sequence of letters is a word. For each set $P$ of six words of 4 letters each, we denote $N_P$ to the set of all words that do not contain any of the words of $P$ as a syllable (subword).
Show that if $N_P$ is finite, then all its words are of length less than or equal to 10, and find a set $P$ such that $N_P$ is finite and contains at least one word of length 10.
Show that if $N_P$ is finite, then all its words are of length less than or equal to 10, and find a set $P$ such that $N_P$ is finite and contains at least one word of length 10.