Levesque has argued that the problem of resolving difficult pronouns in a carefully chosen set of twin sentences, which he refers to as the Winograd Schema Challenge (WSC), could serve as a conceptually and practically appealing alternative to the well-known Turing Test. As he said, probably anything that answers correctly a series of these questions is thinking in the full-bodied sense we usually reserve for people. In this paper we examine the task of resolving cases of definite pronouns. Specifically, we examine those for which traditional linguistic constraints on co-reference as well as commonly-used resolution heuristics are not useful, or the procedure they follow is very similar to a statistical approach, without invoking common logic like humans do.