MathDB

Non-isolated subsets

Source: Baltic Way 2007

November 30, 2010

combinatorics proposedcombinatorics

Problem Statement

Call a set

A

of integers non-isolated, if for every

a\in A

at least one of the numbers

a-1

and

a+1

also belongs to

A

. Prove that the number of five-element non-isolated subsets of

\{1, 2,\ldots ,n\}

(n-4)^2