The Three Gods Puzzle

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#1

There’s a famous logical puzzle by this name (which you better not Google if you intend to solve it, or I’ll beat you up), and I thought it’d be interesting to post it and see if anyone who doesn’t know the solution can solve it! It’s very difficult; you won’t get it right away unless you’re knee-deep in logic theory. But it’s very fun to work with! I’ll choose one of the harder variants for us to work with; if you know the solution, kindly don’t tell anyone or post here!

Three gods A, B, and C are called, in no particular order, True, False, and Random. True always speaks truly, False always speaks falsely, but whether Random speaks truly or falsely is a completely random matter. Your task is to determine the identities of A, B, and C by asking three yes-no questions; each question must be put to exactly one god. The gods understand English, but will answer all questions in their own language, in which the words for yes and no are da and ja, in some order. You do not know which word means which.

Furthermore, the question must have a single truth value (of True or False) regardless of which god you ask it

Easy mode: you may ask no more than 4 questions.

Hard mode: you may ask no more than 3 questions.

Beatrice mode: you must murder no less than all of them. :cackle:

Begin when ready. I’ll be the judge of your responses!

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#2

Well then let me finally present my solution.

Eeeeehhh? Easy Modo?

First let’s look at the following question:

Does da mean yes?

So how can the answers look? If da means yes, then Truth is going to answer da, since the statement is correct and he’s going to answer yes. False would answer ja respectively. If da means no, then Truth would say no, since our statement is false, however, since da now means no, Truth would still answer da. False would still answer ja respectively.
So we ask each god this question. As Random’s answer is random, there are now two cases: Either two gods answered da, or two gods answered ja. Whichever god is isolated gets asked this fourth question. For this question, the two gods that answered the same shall be referred to as X and Y, to not have to write the same thing three times. If it’s Truth, we ask

Is it correct that either da means yes or X is False?

So if ja was the answer then X is False and Y is Random, and if da was the answer it’s the other way around.

Now for if False was isolated by our first three questions:

Is it correct that either da means yes or X is Truth?

If da was the answer, X is Truth and Y is Random, if ja was the answer it’s the other way around.

Hard Mode

You already saw in the easy variant that I used compound subjects to combine several questions into one, so to speak. This’ll be brought to its extreme in this solution.

First I ask A: Is it correct that either da means yes or that B is Truth or C is False?

If da was answered, then only A or C can be Random. If ja was answered, only A or B can be Random.

If da was anwered, I ask the following question to B: Is it correct that either da means yes or that both C is Truth and A is False?

If da was answered, we now know that B is Truth on top of the knowledge we gained from our first question. If ja was the answer, we know that B is False.

So if our second question was answered with da, we ask B: Is it correct that either da means yes or C is False?

If ja was answered, then A is Random, B is Truth and C is False. If da was answered, then A is False, B is Truth and C is Random.

If our second question was answered with ja, we ask B: Is it correct that either da means yes or C is Truth?

If da was answered, then A is Random, B is False and C is Truth. If ja was answered, then A is Truth, B is False and C is Random.

If our first question was answered with ja, we ask C: Is it correct that either da means yes or that both B is Truth and A is False?

If da was answered, C is Truth, if ja was answered, C is False.

So if da was answered, we ask C: Is it correct that either da means yes or B is False?

If da was answered, then A is False, B is Random and C is Truth. If ja was answered, then A is Random, B is False and C is Truth.

If our second question was answered with ja, we ask C: Is it correct that either da means yes or B is Truth?

If da was answered, then A is Random, B is Truth and C is False. If ja was answered, then A is Truth, B is Random and C is False.

I’ll leave Beatrice Mode for someone else if it wasn’t a joke by our dear host.

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#3

Joke Beatrice Solution

[spoiler]Figure out which one is the random answer one. Repeatedly ask them if they did it with the significant other of one of the other gods. Then one of the other God’s would murder the random God.

Then just ask the other gods “Is this statement false?” And then they would self-destruct.[/spoiler]

Now to look up the actual solutions.

Edit: Looks like the idea I got from portal 2 and that tribal sacrifice puzzle was close.

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#4

As you suspected, @VyseGolbez, the answer did lie within complex propositions; once you create a clever few questions, you can just use logic tables to get the correct answer. Well done!

@Dreamheart: there was one variant of the puzzle where their heads would explode if you asked them a question that they could not answer with either da or ja without contradicting their nature. That would kill them pretty well lol

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