Problem solving is a very valuable skill to have, and each of us possess team problem solving to some degree. To teach problem solving skills, you need to set a few challenges or puzzles for the team to solve.
There are several things you need to consider when approaching or creating problem solving activities. One of the first questions that needs to be answered is what is the point of this exercise? What are you trying to Achieve? If you are creating problem solving activities, I find that making the outcome obvious a good way to engage the team. However, you have to make the method require some considerable thinking and experimentation. This is the key to setting problem solving activities.
It is not a challenge if the solution is easy. Another important thing to consider when setting problems is to make the solution appear achievable. Unless your team is full of some strong characters, you may find that everyone gives up. Do you understand the circumstances in which you have to work and solve the problem?