MathDB

A set

S

of integers is Balearic, if there are two (not necessarily distinct) elements

s,s'\in S

whose sum

s+s'

is a power of two; otherwise it is called a non-Balearic set. Find an integer

n

such that

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

contains a 99-element non-Balearic set, whereas all the 100-element subsets are Balearic.

Problem Statement