Does there exist an integer
![n > 1](/media/m/c/8/9/c8999d29e042cf52e485c7a7b7301b0a.png)
which satisfies the following condition? The set of positive integers can be partitioned into
![n](/media/m/a/e/5/ae594d7d1e46f4b979494cf8a815232b.png)
nonempty subsets, such that an arbitrary sum of
![n - 1](/media/m/b/9/f/b9f2e24ffd917df5f63d30599dd3220c.png)
integers, one taken from each of any
![n - 1](/media/m/b/9/f/b9f2e24ffd917df5f63d30599dd3220c.png)
of the subsets, lies in the remaining subset.
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Does there exist an integer $n > 1$ which 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.