With his new riddle of induction, Goodman raised a problem for enumerative induction which many have taken to show that only some ‘natural’ properties can be used for making inductive inferences. Arguably, however, (i) enumerative induction is not a method that scientists use for making inductive inferences in the first place. Moreover, it seems at first sight that (ii) Goodman’s problem does not affect the method that scientists actually use for making such inferences—namely, classical statistics. Taken together, this would indicate (...) that (iii) ‘naturalness’ is not such a relevant concept for the problem of induction, after all. I have no objections against (i) and (iii). But, contrary to (ii), I argue that classical statistics does face a version of Goodman’s problem, which I call the statistical riddle of induction. Given that his problem merely is an instance of the more general problem of underdetermination, this is hardly surprising. Perhaps more importantly, I also show how my riddle can be used for exposing a common fallacy in probabilistic reasoning, without relying on Bayesian assumptions. (shrink)