The FBI has surrounded the headquarters of the Norne corporation. There
are n people in the building. Each person is either an engineer
or a manager. All computer files have been deleted, and all documents
have been shredded by the managers. The problem confronting the FBI interrogation
team is to separate the people into these two classes, so that all the
managers can be locked up and all the engineers can be freed. Each of
the n people knows the status of all the others. The interrogation
consists entirely of asking person i if person j is
an engineer or a manager. The engineers always tell the truth. What makes
it hard is that the managers may not tell the truth. In fact, the managers
are evil geniuses who are conspiring to confuse the interrogators.
- Under the assumption that more than half of the people are engineers, can you find a strategy for the FBI to find one engineer with at most n-1 questions?
- Is this possible in any number of questions if half the people are managers?
- Once an engineer is found, he/she can classify everybody else. Is there a way to classify everybody in fewer questions?
