Traversing Rooms (Difficult!)

An Arab man and an Israeli woman are abducted by extraterrestrials. The E.T.s promise to return them to Earth unharmed, provided that they succeed in the following task: three rooms are designated A, B and C. Each room is square and measures approximately 25 m2. The rooms are connected in such a way that each room has two doors, and each door provides access to one of the other two rooms. The three rooms are acustically isolated and have no furniture or windows. The walls, doors, ceiling and floor of the rooms are solid and opaque, and contain no cracks, holes, hidden passages or the like. The man is placed in room A and the woman in room B. They both receive the following instructions:  
   
1-  They both have 1 hour to traverse the three rooms and return to the room where they started, always walking in the direction A - B - C - A.  
2-  The both have to remain seated, on the floor, in their respective rooms, until a signal would be emitted, indicating that the time count had started. The signal was as follows: on each door there are two lamps (one on each side of the door), and the nearly simultaneous lighting of the all the lamps constitutes the signal. Each lamp is bright enough for a person to notice easily even when he is not paying attention to it.  
3-  The moment that the woman touches the doorknob of a room, the man cannot be in that room any more.  
4-  The moment that the man touches the doorknob of a room, the woman cannot be in that room any more.  
5-  The woman has to get up from the floor after the man.  
6-  The man and woman are not permitted to communicate between each other in any way, or obtain from others any information allowing them to figure out where the other one is. They may not beat the walls or the doors, or try to generate any kind of shock wave. On leaving a room and entering another one, it is required to close the corresponding door. Initially all the doors are closed. Two or more doors may not be open at the same time.  
7-  None of them has a clock or any other instrument that can be used to measure time.  
8-  1 minute before the 1 hour period is up the light signal will be given again, indicating that the time is running out.  
9-  When the 1 hour period is up the man has to be sitting in the center of room A and the woman in the center of room B.  
10-  The woman may only sit down after the man.  
11-  The man is told that the woman is exceptionally intelligent.  
12-  The woman is told that the man is exceptionally intelligent.  

The man and the woman did not know each other and had never been in any contact with each other before. They did not communicate with each other during the whole process (to clarify the matter, it can be told that they both were mute and deaf). The experiment is carried out and they manage to perform the task. The experiment is repeated 10 times and each time they complete the task successfully, making it clear that the first time was not due to mere good luck. Afterwards they are returned to Earth where they convert to Zoroastrianism, get married and live happily everafter! Describe the method they used and the way of thinking of both of them.