Finding an efficient route. The following is a floor plan for another section of Fox River...

Finding an efficient route. The following is a floor plan for another section of Fox River. The situation is the same as in Exercise, except there is now only one door by which the guard can enter the room. Place an exit door in one of the rooms A, B, or C so that the guard can enter by the door marked “Enter,” pass through each door and lock it behind him, and then exit by the door you’ve placed in the plan. Explain why this is the only possible place to locate the door.

Finding an efficient route. Because of Michael’s escape from Fox River State Penitentiary, security procedures are being reexamined. In the following floor plan of a section of the prison, if all the doors are open, is it possible for a guard to enter this section from the hallway, pass through each door locking it behind him, and then exit without ever having to open a door that has been previously locked? (Hint: Model this with a graph where you consider the set of objects to be the rooms and the hallway and that any two rooms are related if they are connected by an open door.)