premise: The seven members of an academic department are each to be assigned a different room as an office. The department members are professors F and G, lecturers Q, R, and S, and instructors V and W. The available rooms are seven consecutive rooms along one side of a straight hallway numbered sequentially 101 through 107. The assignment must conform to the following conditions: Neither instructor is assigned a room next to a professor's room. Neither professor is assigned room 101 and neither professor is assigned room 107. G is not assigned a room next to R's room. W is not assigned a room next to V's room unless R is also assigned a room next to V's room. What is the greatest number of rooms that could be between the rooms to which F and G are assigned?
hypothesis: four