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Maximal length of a sequence

Source: Polish MO second round 2011

February 19, 2012
combinatorics unsolvedcombinatorics

Problem Statement

∀n∈Z+−{1,2}\forall n\in \mathbb{Z_{+}}-\{1,2\} find the maximal length of a sequence with elements from a set {1,2,…,n}\{1,2,\ldots,n\}, such that any two consecutive elements of this sequence are different and after removing all elements except for the four we do not receive a sequence in form x,y,x,yx,y,x,y (x≠yx\neq y).
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