The Hardest Logic Puzzle Ever

This reminds me of the following installment of a webcomic called "Partially Clips":<p><a href="http://partiallyclips.com/2002/09/11/paradox-dragon/" rel="nofollow">http://partiallyclips.com/2002/09/11/paradox-dragon/</a><p>The webcomic version is easily solvable with counterfactuals (I think -- I could be wrong).

I have to say, I have grown to dislike these 'logic puzzles'. I have read 'To mock a mockingbird', and examined several of these puzzles and non of them are actually hard (as in: challenging) once you realize: often you just need simple things: double negation and massive case exhaustion (and especially the latter here is just tedious and not interesting). Often, you just need the case exhaustion.

I really like the trick of determining the identities of 3 gods with just two yes/no questions. Simple, just ask questions that might make their heads explode. :)

Productivity denial of service attack for OCD sufferers.

is it assumed they know each other's identities or not? (you know like the gatekeeper puzzle: "what would he say if I asked him [question]...")

That is a flawed puzzle. Warning, partial spoiler to the bogus solution included here.<p>------------- -------------<p>The solution proposes that for the first question, I turn to god A and ask "Hey, A, if I were to ask you 'Are you Random', would you say 'ja'?"<p>Either A is Random or is not - we have those two cases to consider. Let's consider the case where A is, in fact, Random - only I don't know it yet.<p>The problem, as stated, says that since A is Random, for each question posed to him, he "mentally flips a coin" and then answers as if he were Truth or as if he were Falsity. So while we're considering the case that A is Random, we have two sub-cases to consider: that he will answer as Truth or that he will answer as Falsity. Let us consider the sub-case where A, although Random, will answer as Truth.<p>Finally, we have sub-sub-cases more: perhaps 'ja' means "yes" or perhaps it means "no". And so, we'll consider the sub-sub-case where 'ja' means "yes".<p>So A is Random, has chosen to answer my first question as Truth, and 'ya' means yes. My question (in the bogus solution) is:<p>"Hey, A, if I were to ask (in your current mental state) 'Are you Random?' would you say 'yes'?"<p>God A (who is Random and who will answer this one question as Truth) reasons thusly. He thinks to himself:<p>"If this guy had asked me 'Are you Random', since I have decided to tell Truth, I would answer 'yes' ('ja').' However, that was <i>not</i> the question put before me - a different question was put before me.<p>Random (that's me, A) flips the coin once per question asked. If he were to have asked 'Are you Random' that would have entailed a coin flip separate from the current coin flip. That other coin flip could have gone either way and so, really, I might have answered 'yes' or 'no' ('ya' or 'da').<p>In other words, we made it clear to this guy that he was supposed to ask a simple yes or no question and instead he asked a question to which the only True answer would be 'dajadaja' [god-speak for 'maybe']."<p>At that point, god A would produce from his sleeve the Magic Wand of Heyting (which was manufatured during the god-wars recorded in the book of RejectingTheLawOfTheExcludedMiddle) and smite me for failing to ask a yes/no question after being clearly instructed to do so.<p>In other words, with the proposed (bogus) answer, should A happen to be Random, and his coin come up Truth, and should 'ja' happen to mean 'yes' -- then I will go to my grave never knowing which god is which. (Similar analysis probably applies to other sub-sub-cases.)<p>Very badly framed puzzle (but one that would be hard to frame soundly without giving away the intended answer).

Am I the only one disappointed that this link didn't go to Fermat's Last Theorem?

I generalised this puzzle to any number of gods:<p><a href="http://www.srcf.ucam.org/~te233/maths/puzzles/evenharder.html" rel="nofollow">http://www.srcf.ucam.org/~te233/maths/puzzles/evenharder.htm...</a>

doesn't require very large inferential jumps. just formulate a hypothesis that postulates a unique solution and test it.<p>i'd say the average code base works your brain harder.

I believe the hardest logic test ever actually goes more like this:<p>There are four gods:<p>One always tells the truth.<p>One always lies.<p>One always chooses a random answer.<p>One always stabs people for trying to be clever or asking tricky questions.