JBMO-SL 2011 C5

Answer

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 $A=\{1,2,3, \ldots, 63\}$ .

Dataset text NuminaMath olympiads. Quoted with source.

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