Let $S = \{\{x_{11},x_{12},x_{13}\},\{x_{21},x_{22},x_{23}\}, \ldots, \{x_{n1},x_{n2},x_{n3}\}\}$ and a target $t$. Let $S_i$ be the subset list $\{x_{i1},x_{i2},x_{i3}\}$. Find a subset sum that sums to $t$ such that one and only one element is chosen from each subset list $S_i$. 

I can also imagine this is the same as finding the longest path from $s$ to some sink such that the path costs less than $t$, where the sum of the edges is the same as choosing from each subset list $S_i$.

Is there a name for this problem? Thanks.