Three Gods with a twist

by nomiddlename1 min read2nd Dec 202012 comments

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Hypotheticals
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My goal here is present this riddle and then add a twist which invalidates a portion of the classic solution. I'd like to see what solutions people come up with. The riddle below is copied from here.

Sailing through a thick fog, you come upon a mysterious island shrouded in mist. A towering volcano in the center of the island pierces the clouds, billowing smoke into the sky. You land your boat and set out to ascend the peak. After an arduous climb, you approach the volcano summit, where lava glows red within a vast crater.

Here, you are approached by three gods.

Problem

On the summit of this remote volcano, you realize a few things through divine intervention.

First, you know that one of the three gods always tells the truth, another always lies, and the third will respond to questions randomly. Therefore, let us call the gods True, False, and Random.

The gods speak a different language. They understand all languages perfectly well, but only answer questions with either ja or da, the words for yes and no. You do not know which god is which, and you do not know which word means yes and which word means no.

Finally, you have an existential problem on your hands. You may ask three yes-or-no questions, each one directed to only one god, and only that god will answer with either ja or da. If you can determine the identities of the three gods, they will send you on your way with their blessing, and you can be assured of a prosperous and fulfilled life. If you fail to determine the identities of the gods, however, they will be less generous in their treatment. The volcano pit smokes and glows red beside you.

With your three questions, how do you figure out which god is True, which is False, and which is Random?

STOP HERE TO AVOID SPOILERS BY IMPLICATION

See here for the "classical" solution.

I'd like to add a simple twist. What happens if you're not allowed to ask any of the gods a question about themselves?

At some point I'll give my answer in the comments but I'd like to see what people come up with.

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12 comments, sorted by Highlighting new comments since Today at 5:55 PM
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Couldn't you simply ask the usual questions, but each mention of themselves is replaced by "a hypothetical God whose behavior is either to always tell the truth, to always lie, or to always give a random answer, and whose behavior is not identical to either of the other Gods"?

Under the classical rules, if you ask either True or False "Would you say 'ja' if asked <question>?", then they will say 'ja' if the answer to <question> is 'yes'.

Under the modified rules, this isn't allowed, so we have to instead ask "Would one of the other two gods that is not Random say 'ja' if asked <question>?" This ends up being reversed from above, since you're dealing with True talking about False or vice versa and so you're guaranteed a single-negative rather than a double-negative or non-negative. However, the principal remains that you don't care which word has which meaning or which god you ask as long as it's not Random.


Let (<god>, <question>) mean: Ask <god> "Would one of the other two gods that is not Random say 'ja' if asked <question>?" and assume that 'da' means 'yes' and 'ja' means 'no'.

  1. (god_A, "Is god_C Random?") If 'yes', then god_B is not Random. If 'no', then god_C is not Random.

Let god_NR be whichever of god_B and god_C we just determined is not Random, and let god_MR be the other one.

  1. (god_NR, "Is god_A Random?") If 'yes', then god_A is Random. If 'no', then god_MR is Random.

Let god_NR2 be whichever of god_A and god_MR we didn't just determine is Random.

  1. (god_NR, "Is god_NR2 False?") If 'yes', then god_NR is True and god_NR2 is False. If 'no', then god_NR is False and god_NR2 is True.

This is just the classical solution with a slightly different hypothetical phrasing.

Well done! I had an answer which differs more than the classical answer and wanted to modify the riddle to force my answer but it looks like I I failed at that.

My answer still uses the double negative trick to avoid the need to know what "ja" and "da" mean and goes as follows.
1-Ask god A: "If I asked "is the sky is blue?" to gods b and c is b more likely to tell the truth than c?" Both True and False will say that their non random counterpart is more likely to lie so a negative response means either god A or C is Random and rules out god B. A positive response rules out god C.

2-Ask the god who has been ruled out as being random the same question about the other two gods to figure out which is Random. 

3-Ask one of the non Random gods a question like "is the sky blue?"

I really liked this answer now I just got to figure out how to change the riddle to force it

Consider spoiler-tagging your solution.

One of the properties of the classical solution is that it works even if the Random god is actually an intelligent adversary trying to thwart your strategy. Anything that uses "more likely" language won't be guaranteed to work in that case.

Maybe something like not allowing hypothetical question that you wouldn't be allowed to actually ask would work to force your solution. (So you couldn't ask "would god_X say 'blah' if asked 'are you Random?'", since you couldn't actually ask god_X that question.)

Good point about the classical solution having an advantage. Also, how do you spoiler tag?

If you're using the normal editor, just type >! followed by a space, and a spoiler box should show up.

If you're using markdown, then

:::spoiler
Hidden text here.
:::

yields

Hidden text here.

Thanks. I just looked into this and am reading about what "markdown" is.

Be aware that there is a different (default?) editor that has a different syntax. There's a way to switch between them in your account settings.

What does it mean for a question to be "about" a particular god?

If I can't ask "Are you True?", can I ask "Is neither other god True?"

If I'm talking to True (but I don't know that), can I ask something like "Would True say 'ja' to <question>?", or does that count as a question about the god I'm talking to?

1-You can ask "Is neither other god True."

2-Good point I should have been more clear - You can only ask questions that are definitively not about the god you are talking to. I'll try to edit the post accordingly.