A puzzle about guessing and inquiry

I discuss a puzzle that arises as an apparent tension between plausible theories of good guessing and intuitive constraints on rational inquiry. Clearly, our best guess at a question should reflect the likelihoods we assign to its possible answers. Your best guess is the answer you judge most likely. Additionally, it seems like a requirement of rational inquiry that our guesses be coherent. Thus, our best guess to a constituent (wh-) questions should cohere with our best guess to a polar (yes/no) question whenever answers to the former entail answers to the latter. I argue that these requirements are in conflict and that a familiar form of contextualism doesn't resolve the issue. The puzzle stands as a challenge to existing accounts of rational inquiry and question directed attitudes like guessing.