The Hardest Logic Puzzle Ever

The Hardest Logic Puzzle Ever

I’m not exaggerating; it’s actually called ‘The Hardest Logic Puzzle Ever.’ That just shows you difficult it’s going to be. Are you up for it?

Are you sure?

Okay, then. If you say so. Let’s do this.

So here’s the problem statement:

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A few clarifications: One god can be asked more than one question, a question can depend on the answer to the previous one(s), and Random’s answers do not have some hidden pattern (in other words, they are completely random).

So at first, I bet you were all like, “Yeah, this problem is so easy, whatever,” but then you read the last part. I mean, how can you know which one is which if you don’t know what they are saying or whether they are lying?

To hear the answer, you can watch this video (the riddle is the same, but the background story and names are different). Or, you can read my explanation. Solving this isn’t going to be simple, but let’s go through it step by step.

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First, you need to find a god who is not Random, because Random is unreliable. You can never tell what he’s going to say. You can do this by using counterfactuals in your questions.

 

Counterfactuals are worded in this way: “If I asked you Q, would you respond with ‘ja’?” Q can be any statement you choose. This way, whether the god is lying or not doesn’t matter, because you will get the correct answer either way. Also, it doesn’t matter what ‘ja’ means, because you have achieved the purpose of the question.¬†There are many different counterfactuals that you could ask.

So, for the first question, you should ask god B, “If I asked you ‘Is A Random,’ would you respond with¬†‘ja’?” Then, if B says ‘ja,’ that means that C is not Random, because either A is Random, or B is Random and is answering randomly. And if B says ‘da,’ A isn’t Random because either B or C is Random.

Once you find a god who isn’t Random, you need to figure out whether he/she is True or False. You can do this by asking another counterfactual like the previous one, but with a different statement for Q. You should ask: “If I asked you ‘Are you False,’ would you say ‘ja’?” If the god says ‘da,’ then he/she must be True. ¬†Conversely, if the god says ‘ja,’ then he/she must be False. Now, you know the identity of one of the gods. You can discover who the other two are with your last question.

You should ask the last question to the same god because you know who he/she is. Asking “If I asked you ‘Is B Random,’ would you say ‘ja’?” would reveal who is Random. This is because if the god answers ‘ja,’ then B is Random. If the god says ‘da,’ however, then the god whom you haven’t asked to anything is Random. Then, you can figure out the identity of the last god using elimination.

Now take a deep breath and relax, because we just solved the Hardest Logic Puzzle Ever. Was that mentally challenging or super easy? Maybe you’re a genius in the making. Let me know if you have any questions by commenting or emailing me. Peace out!

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Sources:

  • “The Hardest Logic Puzzle Ever.” Wikipedia. Wikimedia Foundation, 29 Mar. 2017. Web. 23 May 2017.
  • “Can You Solve the Three Gods Riddle? – Alex Gendler.” TED-Ed. N.p., n.d. Web. 23 May 2017.
  • Cuong. Prometheus Journal. N.p., n.d. Web. 23 May 2017.
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