Problem

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Tags: induction, combinatorics proposed, combinatorics



Prove that for arbitary positive integer $ n\geq 4$, there exists a permutation of the subsets that contain at least two elements of the set $ G_{n} = \{1,2,3,\cdots,n\}$: $ P_{1},P_{2},\cdots,P_{2^n - n - 1}$ such that $ |P_{i}\cap P_{i + 1}| = 2,i = 1,2,\cdots,2^n - n - 2.$