Gilligan puzzled out the mystery for a few moments and suddenly was struck with a good test to the nature of the doors. He walked the length of the hallway and came back upon the three doors. He dug into his lunch sack and pulled out his Apple he opened (or perhaps reopened depending on how this goes) the door on the left and gently rolled the fruit through the doorway. He then turned around and came back to the door he had came in at to see if his Apple had tracked back to the start of the room.