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I am referring to the truth, lying and random gods puzzle, linked here (be careful, the solution is in the Wikipedia page!)

https://en.m.wikipedia.org/wiki/The_Hardest_Logic_Puzzle_Ever

Please, DO NOT GIVE THE SOLUTION OR HINTS, I am just looking for clarifications!

I wanted to know :

  • what happens when I am asking truth God about what random God would answer. Is the truth God going to randomly flip a coin to determine the random god possible answer or is the truth God unable to answer and remaining quiet? Thus detecting the random god.

  • how does this random god works? From this detail,

Note that the Random god in Boolos' puzzle is a god who acts randomly as either a truth-teller or a liar. This is different from a god who answers 'yes' or 'no' randomly. One usual trick in solving many logic puzzles is to design a (perhaps composite) question that forces both a truth-teller and a liar to answer 'yes'. For such a question, a person who randomly chooses to be a truth-teller or a liar is still forced to answer 'yes', but a person who answers randomly may answer 'yes' or 'no'.

I think that the usual trick "what your brother would advice" still works, am I right?

  • do the gods know each other language, meaning, is there any language inversion between Gods or do they properly translate each others answer? I am trying to think the puzzle as some electric/logic circuit somehow with No gate and such.

And I think that's it, for now :)

I am sorry to post here such a question, but I need a place where the answer will not be pushed right to my eyes and the kid who forward me the puzzle is not able to help me without spilling part of the beans!

Thank you very much for your understanding.

Edit : I got a better phrasing for the random god : can I say that every time I am asking a question, I have either 2 lying Gods and one truth teller or 2 truth tellers and one liar?

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  • $\begingroup$ Gods know everything no? ;) $\endgroup$
    – Mordechai
    Commented Mar 3, 2017 at 15:15
  • $\begingroup$ "What happens when I am asking truth God about what random God would answer?" Good question! Is Truth God omniscient with respect to the future coin flips in Random God's head? $\endgroup$
    – DyingIsFun
    Commented Mar 3, 2017 at 15:16
  • $\begingroup$ I have never liked questions based on hypotheticals. Most puzzles of this form can be solved without them, and using questions instead of forms like "Are any of the possible scenarios in this list correct"? If the number of possibilities bounded, and the list enumerates, as opposed to describing, the possibilities being discussed, using questions of that form will avoid ambiguity or contradictions. $\endgroup$
    – supercat
    Commented Mar 2, 2023 at 23:13

1 Answer 1

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You have raised a very pertinent question in terms of logic and as always in a connection to it, an equally important question in the realm of psychology.

Random's Behavior is truly worth a deep introspection and I hereby present my explanation as follows, hoping it will be of help to you.

Now Boolos' clarifying remark explains Random's behavior as follows: Whether Random speaks truly or not should be thought of as depending on the flip of a coin hidden in his brain: if the coin comes down heads, he speaks truly; if tails, falsely.

But...

Wait ! Here's a catch...The clarifying remark does not tell us the period or the frequency of these coin tosses...that is, "Does he toss 'individually' or throughout a'session'...But again that calls for a definition of 'session'.It's simple though...It means does he toss for a particular series of questions..or tosses 'individually' , that is, after each and every question is asked...

That shall lead to different modes of consideration for us...

Another possible interpretation of Random's behavior when faced with the counterfactual is that he answers the question in its totality after flipping the coin in his head, but figures out the answer to Q in his previous state of mind, while the question is being asked.If this is the case, a small change to the question above yields a question which will always elicit a meaningful answer from Random.

Please please do note that 'actually tossing a coin' and 'tossing a coin (mentally) or in one's head' are not the exact same. WHY IS THAT ? Since, you seem to be inquisitive and enthusiastic, @Poutrathor , I implore you to realize it yourself using different counterfactuals...

And...

There's virtually no requirement for the Gods to hold prior communication between themselves and comprehending their languages...all you need to do is frame your questions logically. Yeah, realizing an electric circuit in form of boolean logic gates ain't a bad idea...just convolute them simply ;)

Finally,I'd like to say that while your interest at not looking at the solution is a plus, the answer to your question and the golden key to your realization lies in the solution itself...as there will be subtle changes...syntactically in the questions you ask the Gods,...when this edit is imposed...

So I end by citing the edit to Boolos' statement of Random's Behavior by Rabern and Rabern in the year 2008.

Which states...

Whether Random says ja or da should be thought of as depending on the flip of a coin hidden in his brain: if the coin comes down heads, he says ja; if tails, he says da.

You know what ja and da are, don't you ? ;)...

Happy Puzzling.Thank You. :)

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