3 Paths: Doom; Doom; Civilization

Logic Level 1

Path A: Path C leads to civilization.
Path B: Path A is lying.
Path C: Path B leads to doom.

You are lost. There are three paths that branch off of where you stand. One path leads to civilization, while the other two lead to your doom. The path to civilization is truthful, but exactly one path is lying. Which path leads to civilization?

Path A Path B Path C Not enough information

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2 solutions

Christopher Boo
Sep 3, 2016

Relevant wiki: Truth-Tellers and Liars

Suppose Path A is the only one lying, then Paths B and C are telling the truth. Which means, Path C leads to my doom and so is Path B, this leaves us with Path A leading us to civilization. But we are told that the path to civilization is truthful, so Path A does not lead us to civilization, hence is a contradiction.

So now, we know that Path A must be telling the truth, so Path C leads to civilization, which means that Path C must be telling the truth as well. Then Path B must be lying, which is indeed true, because "Path A is lying" is false. Everything checks out, and so Path C leads to civilization.

I don't get why there's a contradiction when path A is lying? It says no where that the path which leads to Doom cannot be telling the truth. Could you explain this to me?

Michelle Ja - 4 years, 7 months ago

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Sorry, I've fixed my first paragraph. Thanks for pointing it out! ;)

Christopher Boo - 4 years, 7 months ago
Autumn Green
Aug 30, 2016

Relevant wiki: Truth-Tellers and Liars

Path B is lying. This can be proved by seeing if the other two make sense and match the problem.
Path A says that path C leads to civilization, while path C says path B leads to doom.
Assuming that paths A and C are truthful, this would put path C as leading to civilization.
This would make sense because it is path B that is lying.
This means Path C meets the requirements and is the correct answer.

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