Testimonial accounts of mathematical problem choice typically rely on intrinsic constraints. They focus on the worth of the problem and feelings of beauty. These are often developed as both descriptive and normative constraints on problem choice. In this paper, I aim to add an extrinsic constraint of no less importance: the assurance of contact of minds with a desired audience. A number of elements for the relationship between mathematician and his audience make up this contact. This constraint stems from the mathematician's role as an arguer, as one of the pre-requisites to argumentation is contact of minds. I examine two exceptional cases which fail to be explained by intrinsic constraints on motivation and posit how this contact could influence usual cases. While not the only constraint or drive in problem choice, establishing contact of minds plays an important role worth further examination.