Question 91
A succession of letters $\overline{l_1l_2\dots l_n}$, where $n \ge 1$, is called a *word*. A word $\overline{l_1l_2\dots l_n}$ is called a *palindrome*, if $l_k = l_{n-k+1}$, for each $k \in \{1, 2, \dots, n\}$.
Consider a two-letter word $X = \overline{l_1l_2\dots l_{2014}}$, with letters $A$ and/or $B$. Prove that $X$ can be obtained by writing one next to another at most 806 palindromes.
Consider a two-letter word $X = \overline{l_1l_2\dots l_{2014}}$, with letters $A$ and/or $B$. Prove that $X$ can be obtained by writing one next to another at most 806 palindromes.