MathDB

Problem 3

Part of 2017 Mediterranean Mathematics Olympiad

Problems(1)

Balearic sets

Source:

6/15/2017
A set SS of integers is Balearic, if there are two (not necessarily distinct) elements s,s′∈Ss,s'\in S whose sum s+s′s+s' is a power of two; otherwise it is called a non-Balearic set. Find an integer nn such that {1,2,…,n}\{1,2,\ldots,n\} contains a 99-element non-Balearic set, whereas all the 100-element subsets are Balearic.
combinatoricsnumber theory