Proving SSum is NP-Complete?
One way to show that SSUM is NP-hard is by reduction from SUBSET-SUM. The idea is to replace each number $n_i$ by two numbers $Mn_i + \epsilon_i$ and $\epsilon_i$, where $M$ is a "large" integer and $\epsilon_i$ is a "small" integer. By varying $\epsilon_i$ you ensure that all numbers are different. You set your target at $MT+\delta$, where $T$ is the original target and $\delta = \sum_i \epsilon_i$. Further details left to you.