MathDB

5

Part of 2011 Junior Macedonian Mathematical Olympiad

Problems(1)

We say that a set $M$ containing $4$ elements is "evenly connected"

Source: Junior Macedonian MO 2011

10/5/2023
We say that a set MM{} containing 44 elements is "evenly connected" if for each element x∈Mx\in M, at least one of the numbers x−2x-2 or x+2x+2 belongs to the set M.M. Let SnS_n be the number of "evenly connected" subsets of {1,2,3…,n}\{1,2,3\ldots,n\}. Find the smallest nn{} such that Sn≥2011.S_n \geq 2011.