The maximum number of winning 2-sets (Q1182325)

In the winning \(t\)-set problem with parameters \(n,a,b,t\) we must choose nonnegative real numbers \(x_ 1,x_ 2,\dots,x_ n\) subject to \(x_ i\leq a\) and \(\Sigma x_ i=b\), so as to maximize the number of \(t\)-sets \(I\) having the property \(\sum_{i\in I}x_ i\geq 1\). For \(t=2\) the author provides a solution by characterizing potentially optimal configurations. For \(t>2\) he conjectures that it remains true that there is always an optimal solution with at most two distinct nonzero values. The winning \(t\)-set problem originated in a sampling without replacement setting and can be formulated probabilistically.