You Can't Agree to Defend, Even if You Have Different Information

For prime numbers, it's clear that even if we have different information, we can't agree to disagree. In a more complicated example, were it's still going to be the case, tit you can't agrees to disagree. All right, so let's explore this further in the context of a fun detective story. So a crime has been committed and the da would like to get it solved. He calls the heads of two investigative units and asks them to please report back with the culprit. Each hed who knows nothing about the case appoints his best detective to the case. The detectives work completely independently and never communicate with each other. They are equally skilled and have received exactly the same training