Problem

Source: JBMO 2011 Shortlist C5

Tags: JBMO, combinatorics, Sets



A set $S$ of natural numbers is called good, if for each element $x \in S, x$ does not divide the sum of the remaining numbers in $S$. Find the maximal possible number of elements of a good set which is a subset of the set $A = \{1,2, 3, ...,63\}$.