The following is a problem posed by Lindenstrauss: "It is easily verified that every separable Banach space has an strictly convex norm. The same is true for a general WCG space. On the other hand, it was shown by Day that there exist Banach spaces which do not have an equivalent strictly convex norm. Some conjectures concerning a possible answer to the question were shown to be false by Dashiell and Lindenstrauss. This results shows that even for C(K) spaces it seems to be a delicate and presumably difficult question to decide under which condition there exists an equivalent strictly convex norm." We shall present a new complete answer to this question.