The ability to solve problems with people of diverse backgrounds is essential for engineering graduates. A course on engineering grand challenges was designed to promote collaborative problem-solving (CPS) skills. One unique component is that students need to work both within their own team and collaborate with the other team to tackle engineering challenges. It is found that the course facilitates the development in CPS skills and that the process, in which two teams develop arguments and integrate the initial ideas to generate a final solution, is a critical component. The value of CPS skills in tackling engineering problems has also been demonstrated. Appropriate scaffolding, explicit training and constant feedback on collaborative processes are found as important for the skill development.