Question 52
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 $\{1, 2, \dots, n\}$ contains a 99-element non-Balearic set, whereas all the 100-element subsets are Balearic.