Finding the Dobbler

Logic Level 2

You are an astronaut who has landed on the planet Sireda 458 to find some species called Dobblers. You are on your way when three mysterious pillars of black smoke come your way. A wise old creature named Hectast leads them. You ask him if he knows the way to the village of the Dobblers when he tells you that hidden in one of the pillars of smoke there is a Dobbler, in one there is a Borsdort and in the other one there is a Kroutiar. He tells you that if you could work out where the Dobbler is hidden he will send the Dobbler to show you the way to the village. You already know that Dobblers always tell the truth, Borsdorts always lies and Kroutiars sometimes tell the truth and sometimes lie. So you ask the first pillar of smoke who is hiding in the second pillar, and you get an answer of 'Borstord'. You ask the second pillar who is hiding in the third pillar, and you get an answer of 'Dobbler'. You ask the third pillar who is hiding in the first pillar, and you get an answer of 'Kroutiar'. So, in which pillar is the Dobbler hiding?

The first The second The third Cannot be told

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2 solutions

Www Www
May 2, 2016

The Dobbler cannot be hiding in the second pillar of smoke, because we know that Dobblers always tell the truth, and if the Dobbler is hiding in the second pillar, he tells us that the Dobbler is hiding in the third pillar. Since the Dobbler cannot be in two places at a time, the Dobbler is not hiding in the second pillar.

If the Dobbler is hiding in the first pillar, then the Borstord should be hiding in the second pillar, since the Dobbler always tells the truth. Because the Borstord always lies, the Dobbler isn't hiding in the third pillar, so the Kroutiar is hiding in the third pillar. Since the Kroutiar sometimes tells the truth and sometimes lies, he lied when he said that the Kroutiar is hiding in the first pillar.

If the Dobbler is hiding in the third pillar, he says that the Kroutiar is hiding in the first pillar, which must be true. The Kroutiar then says that the Borstord is hiding in the second pillar, which is true, and since the Kroutiar can either tell the truth or lie, we're OK so far. But the Borstord says that the Dobbler is hiding in the third pillar, which is true, and since the Borstord always lie, the Dobbler cannot be hiding in the third pillar. So the Dobbler must be hiding in the first pillar.

Nice explanation. I would suggest that you split the problem and the solution into multiple paragraphs. Right now, it is difficult to read such a big chunk of text.

Pranshu Gaba - 5 years, 1 month ago
Saya Suka
Feb 16, 2021

We were told of a 3-period cycle of 2B --> 3D --> 1K --> 2B. Even though each of them didn't say anything that's obviously contradictory, that doesn't mean that we can trust everything, since we were already told that there's a pathological liar among the 3, so at least one of these answers must be a lie. Also, with a generally honest truth teller among the 3, at least one of these answers must be a truth. So, this cycle told to us must have 1 fixed truth told by the only truth teller and the other 2 (Borstord & Kroutiar) must have lied and exchanged their answers. Thus, we know NOT to trust the statement when one of the liars introduce the truth teller to us (since truth teller cannot do the self-identificaton with the kind of question posed to them), with their claim of a Dobbler at the 3rd pillar. Thus, the Dobbler must be at the 1st pillar, who truthfully identified the Borstord at 2nd pillar and finally the Kroutiar at the 3rd pillar.

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