\emph{Bidirectional typing} and \emph{constraint-based type inference} have complementary strengths on type checking and deducing types for partially annotated programs. This paper develops \emph{type hole inference}, which combines benefits of \emph{bidirectional typing} and \emph{type inference}. Our approach has a simple typing algorithm, simple error messages, and explicit annotations in the same situations that bidirectional typing does. However, programmers don’t have to actually fill out all of those explicit annotations, most of which are inserted and inferred automatically.