After winning the Fairy Logician's competition, you are reverse-summoned to a room with 5 portals at equal distances from each other. They are all locked,but fortunately, there is a logical demon in front of each portal, they are willing to unlock one portal for you. The problem is that only 1 of these portals is the exit while the others will send you to your certain death.
The demons are all knowing, but incredibly lazy. They will only allow you to ask 3 questions. They will only provide a 1-bit (yes/no) answer. And if your question requires more than 25 english words* to perfectly grammatically express they won't answer it.
Oh yeah, one more thing, though demons are supposed to lie, all but one of them are to lazy to too that, and will answer truthfully.
Can you get out alive, Logician Adventurer?
(*) words are all you can use, expressions like ∀ε ∃δ have to be expressed like this: "There is a delta for every epsilon", which is 7 words already, and you have 25.
Disclaimer: this puzzle is based heavily on the one by stack reader
Answer
Pick any demon.
1. If I asked you if one of these 3 portals (point) was the exit, would you say yes?
Because the question loops itself, it doesn't matter if the devil is a liar or not, they will be telling the truth, and I'll know which group, of either 2 or 3 portals, the exit is in. Point to one of the portals from that group. Ask any devil.
2. If I asked you if this was the exit, would you say yes?
Again, loops itself, doesn't matter if the devil's a liar. If it's the exit, we can leave. If it isn't, and this is the group of 2 portals, we know the other is the exit. If this is the group of 3 portals, we have to point at one of the remaining ones, and ask any devil.
3. If I asked you if this was the exit, would you say yes?
Now we know, and can leave.
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