Source location privacy is becoming an increasingly important property in wireless sensor network applications, such as asset monitoring. The original source location problem is to protect the location of a source in a wireless sensor network from a single distributed eavesdropper attack. Several techniques have been proposed to address the source location problem, where most of these apply some form of traffic analysis and engineering to provide enhanced privacy. One such technique, namely fake sources, has proved to be promising for providing source location privacy. Recent research has concentrated on investigating the efficiency of fake source approaches under various attacker models. In this paper, we (i) provide a novel formalisation of the source location privacy problem, (ii) prove the source location privacy problem to be NP-complete, and (iii) provide a heuristic that yields an optimal level of privacy under appropriate parameterisation. Crucially, the results presented show that fake sources can provide a high, sometimes optimal, level of privacy.