IMO 1993 - Shortlisted Problems Question 18

(POL 1) Let $S_n$ be the number of sequences $(a_1,a_2,\ldots,a_n)$, where $a_i\in\{0,1\}$, in which no six consecutive blocks are equal. Prove that $S_n\to\infty$ as $n\to\infty$.