Question 21
N7 (BLR). Does there exist an integer $n\gt 1$ that satisfies the following condition?
The set of positive integers can be partitioned into $n$ nonempty subsets such that an arbitrary sum of $n-1$ integers, one taken from each of any $n-1$ of the subsets, lies in the remaining subset.
The set of positive integers can be partitioned into $n$ nonempty subsets such that an arbitrary sum of $n-1$ integers, one taken from each of any $n-1$ of the subsets, lies in the remaining subset.