Nelson Goodman on Induction

Suppose I am entertaining the following hypothesis: “All swans are white.” So long as I see no non-white swans, each instance of a white swan I see serves to confirm this hypothesis. Suppose that I also am entertaining a different hypothesis: “All people with black shirts have three brothers.” So long as I haven’t encountered a black-shirted individual without three brothers, does a particular instance of a black-shirted person with three brothers serve to confirm this hypothesis?
Nelson Goodman, in his paper “The New Riddle of Induction” thinks that there is something quite different going on in the first case than in the second. The swan hypothesis appears to be “lawlike”, whilst the second hypothesis appears to be merely “accidental.” Goodman’s challenge in the paper is to determine some clear demarcating features that distinguish law-like hypothesis from he takes to be accidental hypothesis. The upshot of such a project, he thinks, is for us to get clear as to which hypotheses are such that they can be confirmed by particular cases, in such a way that could ultimately lead us to be justified in accepting these hypotheses.
The new “riddle” of induction amounts to the challenging of determining such demarcating features. Goodman makes it clear in his paper that this is not a simple challenge. I am interested to know this: (1) what is the best answer to Goodman’s riddle? (2) What answer have most people accepted to this riddle?
I think that an adequate answer to Goodman on this score is of comparable importance to the epistemic project as is an adequate answer to Chisholm’s problem of the criterion; this is because both challenges threaten (in different ways) the possibility of knowledge. In the case of Goodman’s riddle, what is up for grabs is decisively inductive knowledge, on which much of what we take to be our scientific knowledge rests.