In the final exercise of the day and with trepidation aforethought, I assigned two people who were fierce adversaries to the same team. I feared that they might lash out at each other. I needn't have worried. Moments into the exercise, I heard one of them say to the other, "You went to college there? So did I."
I don't know how the subject came up, but suddenly—and perhaps for the first time—these two individuals saw each other not as adversaries but as human beings—people who had lives separate from work, lives not altogether different from their own. In no time, these two individuals found themselves reminiscing, laughing about their shared past, and playing "Did you know...?" They suddenly realized that, for all their differences, they also had things in common.
The discovery of things in common didn't dissolve all the problems among these four groups, but it was a stepping stone. By the end of the session, the four groups had learned a lot about each other and had identified some of their biggest obstacles in working together. And, at their own request, they had developed a list of steps they wanted to take to learn more about each other's work and to help each other.
This type of relationship strengthening is not at all unusual when you're getting to know each other better.