The conventional approach for testing distributions equality in the classical two-sample problem is based on the difference between the two empirical distributions. We consider the problem of testing distributions equality when the observer is "color blind" so he cannot distinguish the distribution that generated each measurement in the observed pairs. Within a non-parametric framework, we construct an empirical process for this problem and find the asymptotically optimal test statistic for a particular sequence of local alternatives. The talk is based on joint work with Estate Khmaladze.