Fault localization helps spotting faults in source code by exploiting automatically collected data. Deviating from other fault locators relying on hit spectra or test coverage information, we do not compute the likelihood of each possible fault location by evaluating its participation in failed and passed test cases, but rather search for each failed test case the set of possible fault locations explaining its failure. Assuming a probability distribution of the number of faults as the only other input, we can compute the probability of faultiness for each possible fault location in presence of arbitrarily many faults. As the main threat to the viability of our approach we identify its inherent complexity, for which we present two simple bypasses. First experiments show that while leaving room for improvement, our approach is already feasible in practical cases.