Question 71
The venusian prophet Zabruberson sent to his pupils a 10000-letter word, each letter being $A$ or $E$: the *Zabrubic word*. Their pupils decided that, for $1 \le k \le 10000$, each word comprised of $k$ consecutive letters of the *Zabrubic* word is a *prophetic word* of length $k$. It is known that there are at most 7 prophetic words of length 3. Find the maximum number of prophetic words of length 10.