olymmath

JBMO-SL 2018 C1

  • Answer

A set SS is called neighbouring if it has the following two properties: a) SS has exactly four elements

b) for every element xx of SS, at least one of the numbers x−1x-1 or x+1x+1 belongs to SS.

Find the number of all neighbouring subsets of the set {1,2,…,n}\{1,2, \ldots, n\}.

Dataset text NuminaMath olympiads. Quoted with source.

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\frac{(n-3)(n-2)}{2}

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