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?
For example:
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.
Answer
To the best of my knowledge, it is impossible to have an infinite loop when starting on the far left.
The best reasoning I can provide is that once you enter the first door, it is impossible to ever enter that door again from the left. Since your loop is already 'breaking', you'll then never be able to enter the path between the second A-B again.
Ultimately, you run into the case where you will only ever walk the path between the two letters once. A good way to look at this is to consider the Start/End as a pair of doors themselves.
[Start] [You] A D B A C B C D ... [End]
In the long run, the only loop you're bound to be stuck in is the one you started between, which in this case is the losing factor.
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