Problem

Source: Baltic Way 1998

Tags: combinatorics proposed, combinatorics



Determine all positive integers $n$ for which there exists a set $S$ with the following properties: (i) $S$ consists of $n$ positive integers, all smaller than $2^{n-1}$; (ii) for any two distinct subsets $A$ and $B$ of $S$, the sum of the elements of $A$ is different from the sum of the elements of $B$.