This paper presents an example of incorporating a research problem in a course - Numerical Methods for Mechanical Engineers. In bascule bridges, the fulcrum is assembled by shrink-fitting a trunnion into a hub. In one case, the trunnion cooled in a dry-ice/alcohol mixture for shrink fitting got stuck halfway in the hub. Answering the question why the trunnion got stuck in the hub and finding a solution to the problem, involved numerical solution of mathematical procedures including nonlinear equations, simultaneous linear equations, interpolation, regression, integration, and ordinary differential equations. Students and faculty highly appreciate using this problem-centered approach to teaching the course.