Assume you have an unlimited but finite number of linking, teleporting doors you can add to a hallway of finite length. Assuming there's a door at the start and finish, can you arrange the teleports so that one can never make it to the end of the hallway?
A B A B
Where when you enter A from the left (you'll never turn and enter from the right) you come out of the other A on the right. So you'd enter the first A, come out of the second, enter B come out of the other, hit A again, and when you exit the other and hit B you've got to the end.
You HAVE to start before the first door, and every tele door HAS to have a linking door. No combining links (AB would not have a 50 - 50 chance of A or B) and no more than 2 links, so no random linking.
Can you arrange the tele doors in such a way, you'll never reach the end? If so, how many tele doors does it require, and what's the setup? If not, prove it's impossible.