In his 1972 book : Objective Knowledge, Popper devotes Chap. 1 to the problem of induction. Elsewhere in the book (in Chaps. 3, 4, 6 and 8), he presents a general schema of problem solving. The aim of this paper is to bring these two strands of thought together. The initial problem (P1) is here the traditional philosophical problem of induction. Popper proposes a tentative solution (TS) to this problem. The paper then proceeds with the problem solving schema by adding error elimination (EE), i.e. criticisms of the tentative solution. These are concerned with computer induction, and with the claim that corroboration is in some sense inductive. This discussion leads in turn to the emergence of a new problem (P2). A suggestion is made about how this new problem might be tackled. The approach involves Neurath's principle, but applied to methods rather than theories.