Knowing if there are two solutions to the subset sum problem
Your (self) answer is ok, but you can also build a reduction in which there is no &quot;trivial&quot; solution.
Start from $X = \{ x_{1}, \ldots, x_{n} \}, x_i &gt; 0$ with target sum $K$ and build:
$X' = \{  8 * x_{1}, \ldots, 8 * x_{n} \} \cup \{ 1, 1, 2 \}$ and target sum $K' = 8*K + 2$
In this case in order to solve the new problem $\langle X', K' \rangle$ you are &quot;forced to solve&quot; the original one, and there are at least two solutions to $\langle X', K' \rangle$ if there is a solution to $\langle X, K \rangle$.