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at least 806 palindrome words to stick for a palindrome of 2014 letters

Source: Danube 2014 junior p2

July 22, 2019
palindromescombinatorics

Problem Statement

We call word a sequence of letters l1l2...ln‾,n≥1\overline {l_1l_2...l_n}, n\ge 1 . A word l1l2...ln‾,n≥1\overline {l_1l_2...l_n}, n\ge 1 is called palindrome if lk=ln−k+1l_k=l_{n-k+1} , for any k,1≤k≤nk, 1 \le k \le n. Consider a word X=l1l2...l2014‾X=\overline {l_1l_2...l_{2014}} in which lk∈{A,B} l_k\in\{A,B\} , for any k,1≤k≤2014k, 1\le k \le 2014. Prove that there are at least 806806 palindrome words to ''stick" together to get word XX.
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