Question 170
Find all positive integers $n$ with the following property: the numbers $1, 2, \ldots, n$ can be split into three disjoint non-empty subsets with mutually different sizes such that, for any pair of subsets, the subset with fewer elements has the larger sum of its elements.
(The size of a subset is the number of its elements.)
(The size of a subset is the number of its elements.)