IMO Shortlist 1993 problem C5
Dodao/la:
arhiva2. travnja 2012. Let
![S_n](/media/m/c/2/e/c2e97c6b8d807599d8398c14e4ac95fc.png)
be the number of sequences
![(a_1, a_2, \ldots, a_n),](/media/m/e/f/a/efafc316529c23a50fd57e73381d2946.png)
where
![a_i \in \{0,1\},](/media/m/3/0/b/30bca93fae4c0bc3d6da0130af6efcbf.png)
in which no six consecutive blocks are equal. Prove that
![S_n \rightarrow \infty](/media/m/8/f/1/8f192443e2bd94fb6ee16e1d7acff344.png)
when
%V0
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 $S_n \rightarrow \infty$ when $n \rightarrow \infty.$
Izvor: Međunarodna matematička olimpijada, shortlist 1993