Popper famously claimed that he had solved the problem of induction, but few agree. This paper explains what Popper's solution was, and defends it. The problem is posed by Hume's argument that any evidence-transcending belief is unreasonable because (1) induction is invalid and (2) it is only reasonable to believe what you can justify. Popper avoids Hume's shocking conclusion by rejecting (2), while accepting (1). The most common objection is that Popper must smuggle in induction somewhere. But this objection smuggles in precisely the justificationist assumption (2) that Popper, as here undestood, rejects.