Let be an integer. Prove that there exists a set of positive integers satisfying the following property: For every the set can be partitioned into two subsets with equal sums of elements, with one of subsets of cardinality .
Let $n\geqslant 3$ be an integer. Prove that there exists a set $S$ of $2n$ positive integers satisfying the following property: For every $m=2,3,...,n$ the set $S$ can be partitioned into two subsets with equal sums of elements, with one of subsets of cardinality $m$.
Školjka 
be an integer. Prove that there exists a set 
of 
positive integers satisfying the following property: For every 
the set 
.