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Poland goes Combinatorics

Source: IMO Shortlist 1993, Poland 1

March 25, 2006
inductioncombinatoricsRamsey TheoryPermutation patternspatternIMO ShortlistPoland

Problem Statement

Let SnS_n be the number of sequences (a1,a2,…,an),(a_1, a_2, \ldots, a_n), where ai∈{0,1},a_i \in \{0,1\}, in which no six consecutive blocks are equal. Prove that Sn→∞S_n \rightarrow \infty when n→∞.n \rightarrow \infty.
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