Nomen postulates:
Following his instructions, you leave the entry room for a few minutes, while the explorer enters one of the passageways. You then re-enter the room, and loudly call out one of the passageway numbers, either 1 or 2. In a few minutes, the explorer comes out of the requested passageway. You then leave the cave and repeat the process many times. Each time, the reporter enters one of the passageways unknown to you; when you return and name one of them, he is able without fail to exit from the named passage.
You reason that if there were no connection between the passageways, the only way the explorer could come out the passage that you named would be if he had gone in that same one. He would have to guess which one you were going to choose, and if he were right, he could come out that one. But you have repeated the test dozens of times. The chances that someone could guess right so often is infinitisimal. The only logical explanation is that the passageway does exist.
A more interesting question would be: If there is no connection between the passageways, and if the explorer manages to pick the passage you are going yell out correctly a large number of times, would you be better off betting or not betting $1 against him being able to do it again at 1000:1 odds. -- Eric Michael Cordian 0+ O:.T:.O:. Mathematical Munitions Division "Do What Thou Wilt Shall Be The Whole Of The Law"