<p>I present a puzzle about inquiry and discuss two potential solutions. The puzzle stems from two equally compelling sets of data suggesting that, on the one hand, there’s something epistemically defective with inquiring into questions that don’t have true answers. On the other hand, however, there can be scenarios in which we are epistemically permitted to inquire into questions that don’t have true answers. How is it that inquiries into questions that don’t have true answers can both be defective and permissible from an epistemic point of view? The first solution I consider maintains that inquiries into questions that don’t have true answers are always impermissible but can be excusable. The second solution maintains that inquiries into questions that don’t have true answers are bad inquiries that can be conducted by inquirers we can legitimately trust. I argue against the former and in favor of the latter.</p>