I just happened to see this story appear in our #rss-bot feed. How to Solve the World's Hardest Logic Puzzle. Given that this is the weekend, I thought it might make for an interesting challenge and discussion.
To set the stage for the puzzle, the author provides some background on Raymond Smullyan, the puzzle's composer:
While a doctoral student at Princeton University in 1957, studying under a founder of theoretical computer science, Raymond Smullyan would occasionally visit New York City. On one of these visits, he met a "very charming lady musician" and, on their first date, Smullyan, an incorrigible flirt, proceeded very logically—and sneakily.
"Would you please do me a favor?" he asked her. "I am to make a statement. If the statement is true, would you give me your autograph?"
Content to play along, she replied, "I don't see why not."
"If the statement is false," he went on, "you don't give me your autograph."
"Alright ..."
His statement was: "You'll give me neither your autograph nor a kiss."
It takes a moment, but the cleverness of Smullyan's ploy eventually becomes clear.
A truthful statement gets him her autograph, as they agreed. But Smullyan's statement, supposing it's true, leads to contradiction: It rules out giving an autograph. That makes Smullyan's statement false. And if Smullyan's statement is false, then the charming lady musician will give him either an autograph or a kiss. Now you see the trap: She has already agreed not to reward a false statement with an autograph.
With logic, Smullyan turned a false statement into a kiss. (And into a beautiful romance: The two would eventually marry.)
Clever! But enough with the setup — What's the puzzle?
The Hardest Logic Puzzle Ever goes like this:
Three gods A, B, and C are called, in some 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.
The story's author is, himself, a bit of a puzzle-poser. The story tells how to solve the puzzle, but does not actually provide the solution. Are there any Soylentils up to the challenge?
(Score: 5, Insightful) by Ethanol-fueled on Sunday October 23 2016, @04:57PM
Fuck no. We had to do a lot of these types of problems in discrete math, and they blow ass. Of course, that's just my opinion.
(Score: 3, Funny) by Anonymous Coward on Sunday October 23 2016, @05:11PM
I agree. Logical thinking is for liberals, communists, and activists. TRUMP 2016!
(Score: 1, Touché) by Anonymous Coward on Sunday October 23 2016, @05:40PM
I contend that trumpkins are just as logical as anyone else.
They just start with fatally flawed premises.
Garbage in, garbage out.
(Score: 0, Funny) by Anonymous Coward on Sunday October 23 2016, @07:20PM
Sorry, we can't all be such wonderful tolerant geniuses that we believe electing the blatantly obvious criminal wife of a serial rapist, who both already sucked America dry and is leeching off the corpse is a good idea.
(Score: 2, Touché) by Anonymous Coward on Sunday October 23 2016, @09:07PM
All we can hope is you get enough sense to realize that Hillary's flaws are no reason to vote for Trump's.
(Score: 2) by edIII on Monday October 24 2016, @01:14AM
Yep. Neither are prizes, nor fountains of morality, nor pillars of community trust.
It's a choice between a highly mentally unstable sexual predator with delusions of grandeur that exhibits scary tendencies towards belligerent and intractable vindictiveness punctuated by childish petulance....
and
a fairly nasty woman who absolutely is an elitist and as die hard of a believer as Trump that the elites are the noble cure to the world. The unwashed masses and labor merely need to be contained, controlled, and profited from. Plenty of evidence for this clear pattern of behavior on her part.
I'm voting for Hillary because Trump would be qualitatively and objectively worse to a very large and substantial degree. Not happy about it, but this is one fucked up choice. I would rather work with the new Democratic platform than the shitstain of ideas coming out of the Republican party. That platform couldn't be more bigoted, close-minded, and backasswards.
Either way may not make a difference. Trump has riled his base up so much with seething mistrust of government and epic levels of disenfranchisement. Those people are prepping for civil war, and at no point in our history have we heard more talk about it. Especially from presidential candidates, governors, and affiliated white nationalist and militant organizations.
It's fucked.
Technically, lunchtime is at any moment. It's just a wave function.
(Score: 2, Disagree) by Farkus888 on Monday October 24 2016, @02:52AM
Speaking of Garbage in Garbage out. Your garbage knowledge of history lead to you making a garbage comment. The American people have had 2 civil wars. I could see you overlooking the revolutionary war being a civil war since we were part of the british empire but fighting against it. America won and pretends they were never really in charge now. The other is literally called the civil war and you should know about it.
(Score: 4, Insightful) by edIII on Monday October 24 2016, @07:27AM
Well.... okay. I'll tell you what I know.
The Civil War had nothing to do with government mistrust, nor disenfranchisement *with* government. So excluding the Civil War, there has been no other time in history. Even during the Civil Rights marches and times of nationwide general strikes, there has not been as much fervor with replacing the government with an outsider, and eliminating the status quo and ideological opposition by whatever means.
Calm down, buddy. There is a difference between knowlege and interpretation of it. We have differing views perhaps, but my knowledge of history is quite adequate.
We never were though. From the beginning what we fought was rich monied interests in England manipulating our economy. They were attempting to stranglehold us while delivering the lions share of the fruits of our toil to the elites in England. Classic exploitation, starting upwards from chattle slavery through peonage and our modern day wage slavery in its advanced forms.
Did the exploitation stop? Did the common American man at the time escape such fates?
No. History shows that quite clearly with a cyclic Capitalistic economy utterly opposed to their interests, those being the interests of the common worker at every single step. Whatever niceties we have now are not because of the inherent morality of the elites in recognizing them, or granting them, or even providing it without commentary. Their commentary often came in the form of fantastic and violent abuses leveraging police, military, and the courts to keep Capitalism on track.
History shows us this. We were never in charge.
The Civil War was fought because of two opposing forces of monied interests. Southern had near complete and assured control over government, while Northern interests were being neglected in favor of repaying English debt owed by the South. Economies at the time were dependent upon cotton and competed with Egypt. When Northern interests captured the influence of the government they immediately shifted the balance of trade by imposing tariffs designed to promote Egyptian cotton and force the disparate economies of the North and South to come under one rule, and one economy, and ONE group of monied interests served.
Slavery is to the Civil War as humanitarianism was to the freeing of Kuwait in the 1st Persian Gulf war. Sounds good and noble, but the truth was that the black man was too much competition to the white man already fighting European immigrants brought over by their own troubles as much as the monied interests desire for imported peonage. 3 forces, or 4 depending on how you count were played against each other. As Jay Gould said, "I can hire one half of the working class to kill the other half".
As Gould is burning in hell, his insight proves that from the very beginning it wasn't a people divided fighting each other, but a small group of men exhorting great influence and causing it to happen. There is a documentary similar to it called Trading Places.
The interests of the black man were just as much aligned with the interests of the white man, and the immigrants, and this was recognized by the rising working force throughout the Industrial Revolution. They called the North the UNION forces for a reason. Entire worker Unions emptied out to leave and free the slaves as much as it was to end the death grip that Northern monied interests had upon them.
Nobody at the time was confused that government had anything to do with it. They KNEW it was corrupt as fuck, just as we do today about ours.
You misunderstood me. I didn't mean to imply that never before has there been more talk about Civil War, but never before has there been more seething mistrust by government by ALL sides at the same time. I don't think slaves underlying hatred against their masters counted, and they were not free to participate save those that escaped to the North.
This is truly different this time as the target of the revolution is actually against the government itself (a local one, not a foreign one), big corporations, and now apparently the media thrown into boot. If a sizable chunk of this radicalized segment of the Republican party become militant they will not be targeting progressives or Democratic citizens, but the edifices and institutions of government itself.
From the other side with an unlikely Trump win, you have over half of the United States so disenfranchised with government and completely opposed to the charter of the Republican Party. When Trump fails to support the working class and repeats ol' Abe's impressive gang raping of America in the largest unearned money grab of all time, America will break.
If Trump has said anything right, it's that America is a complete fucking disaster and not the greatest country in the world right now. The Democrats are being disingenuous and stupid by saying America is already the greatest and getting better. Objectively, we've only been getting worse, and it's about to get a whole lot more worse. As we're already strained so highly with social services and increasing measures of austerity, we've become a forest thick with dangerous tinder.
All it takes is a spark.
How many more jobs we will lose next year that are replaced by jobs pimpled teenagers subsidized by their parents? How many more parents can be subsidized by their parents? How many of those shit jobs will be replaced by automated kiosks that complete the circle bringing back defacto electronic chattle slavery competing with the working force again?
(Score: 0) by Anonymous Coward on Monday October 24 2016, @03:13AM
> The unwashed masses and labor merely need to be contained, controlled, and profited from. Plenty of evidence for this clear pattern of behavior on her part.
And any evidence to the contrary? Or does that not count?
(Score: 2) by edIII on Tuesday October 25 2016, @02:21AM
There is extremely little evidence to the contrary. Other than her recent push to create Progressive policy, which can still be interpreted cynically, no.
Listen to her speeches. Read what Wikileaks had provided. It's not a fatal blow, or even perhaps especially scandalous, but it shows how she feels about the average person versus the elites. One person in public, one person in private (read: in the company of the elites). That's fucking terrible.
Her 6 years as a board member of Wall Mart don't do her any favors. She never spoke up, or against the worker, but in fact helped anti-union activities.
In the past when she tried to give us health care, she was beaten down brutally.... but instead of continuing to fight for us she joined the other side of the health care debate. She took money from them.
Very little in her favor other than im-not-Trump.
Technically, lunchtime is at any moment. It's just a wave function.
(Score: 2) by cubancigar11 on Monday October 24 2016, @10:36AM
"I will vote for a fascist criminal who bribed her way out of judiciary because the other guy is celebrity who gets more sex than me." - edIII (791)
(Score: 0) by Anonymous Coward on Monday October 24 2016, @12:26PM
Yeah, because there are only two candidates you can vote for. Oh, wait …
(Score: 2) by cubancigar11 on Monday October 24 2016, @02:30PM
Oh I am sorry, I thought this more than yet another 'lets bash a successful man who isn't me' thread.
(Score: 2) by edIII on Tuesday October 25 2016, @02:27AM
He isn't successful, but a con man. We don't refer to criminals as successful.
Interesting, that despite his monstrous character flaws (pun intended), that you think objections must simply be due to jealousy.
I can see the level of intelligence you possess, and no, I will no be joining you in the kiddie pool to play around :)
Technically, lunchtime is at any moment. It's just a wave function.
(Score: 2) by cubancigar11 on Tuesday October 25 2016, @01:04PM
Going to vote Hillary because Trump is a criminal. I suppose some people really really like the Ministry of Truth.
(Score: 2) by edIII on Tuesday October 25 2016, @02:24AM
I will fully admit he gets WAY more non consensual sex involving assault then I do, Sure :D
Other than that, you made no substantive points whatsoever and effectively were nothing more than a monkey flinging poo around.
Bad Monkey!
Lol
Technically, lunchtime is at any moment. It's just a wave function.
(Score: 0) by Anonymous Coward on Sunday October 23 2016, @09:08PM
Exactly what I'm talking about!
(Score: 1) by Francis on Sunday October 23 2016, @07:21PM
Seems kind of dull to me, but then again I'm not the sort to drink until things get interesting.
(Score: 1, Insightful) by Anonymous Coward on Sunday October 23 2016, @05:38PM
We are tech. There are no gods, hence there is no one to ask so no answers so no solution. Null set
(Score: 1) by Ethanol-fueled on Sunday October 23 2016, @05:44PM
You could also say that, due to the properties of the null set, the existence of gods is vacuously true.
Thank you, thank you, I finally understand why mathematicians aren't very funny.
(Score: 2) by Bot on Sunday October 23 2016, @06:01PM
1. nobody put forth the hypothesis that those gods actually exist.
2. the concept of existence is at odds with transcendental attribute of the hypothetical god, which makes it meta-existing.
3. science and logic cannot get to divinity any more than supermario can exit his videogame world and chat with you.
brought to you by the SIATAWTJW - Stop Illogical Atheists They Are Worse Than Jeovah Witnesses.
Account abandoned.
(Score: 0) by Anonymous Coward on Monday October 24 2016, @09:44AM
(Score: 0) by Anonymous Coward on Monday October 24 2016, @12:31PM
Eyahouveihau!
(Score: 1, Insightful) by Anonymous Coward on Sunday October 23 2016, @05:39PM
It is not the hardest.
By merely reversing the solution one could extrapolate a problem involving billions of gods and lots of questions.
Or formalise a huge 3-sat problem into natural language and ask a hapless human to solve it with a pen and paper.
Or something similar.
This is just one of those artificial problems people create that is easier to solve once you know the method. Nice brain exercise, nothing more.
(Score: 5, Interesting) by PizzaRollPlinkett on Sunday October 23 2016, @06:17PM
Smullyan's problems seem, to me, to be too clever for his own good. I'm not sure they're even deterministically solvable. I have seen others of his (not this one) where his given solutions are contrived. He typically solves his own puzzle with elaborate and confusing truth tables. Frankly, this stuff probably turns more people away from logic and discrete math than it attracts. If logic is just a confusing tangle of nonsense, what's the point? I'd rather read a witty logic book by W.V. Quine or something.
The only thing worse than Smullyan was Joe Dever in his Lone Wolf books, where he tried to add puzzles like these to exercise the reader's brain, but he mostly managed to outsmart himself. There's one puzzle about a guy's daughter and her siblings that is so confused that I haven't figured it out in 30 years. Apparently, given the answer, her siblings don't consider her to be one of their siblings, which doesn't make sense. Few of his puzzles made much sense, other than the really obvious arithmetic ones.
(E-mail me if you want a pizza roll!)
(Score: 0, Funny) by Anonymous Coward on Monday October 24 2016, @12:58PM
Ugh, another Internet "expert."
(Score: -1, Troll) by Anonymous Coward on Sunday October 23 2016, @06:31PM
ho ho ho, bitches
(Score: 1, Funny) by Anonymous Coward on Sunday October 23 2016, @06:33PM
with the title
Does This Headline Conform With Betteridge's Law?
But then I couldn't think of any body content for TFS.
(Score: 2) by JNCF on Sunday October 23 2016, @08:12PM
Does the Other Headline Conform With Betteridge's Law If and Only If Two Plus Two Equals Four?
(Score: 1, Funny) by Anonymous Coward on Sunday October 23 2016, @06:38PM
Favored by a certain Presidential candidate:
Walk up to the girl you've never met and kiss her on the lips. Then ask,
Are you going to tell lies about what I just did?
(Score: 0) by Anonymous Coward on Sunday October 23 2016, @06:45PM
I suspect the solution involves asking the gods themselves about what they think the other gods would say. Not interested in spending my time reading the article or working out the details.
In the real world liars and false "gods" tell the truth and not randomly :).
Even something like the rock-paper-scissors bot ( http://www.nytimes.com/interactive/science/rock-paper-scissors.html?_r=0 [nytimes.com] ) seems more interesting - go ahead try to beat the RPS bot in advanced mode (I kept the lead for about 20+ rounds but then the counter-counter-counter etc strategy stuff started to make my head hurt, and I figured I would eventually lose :) ).
If you can keep beating the RPS bot you're solving an evolving puzzle that keeps making itself harder for you.
(Score: 0) by Anonymous Coward on Sunday October 23 2016, @06:47PM
(Score: 2) by tangomargarine on Monday October 24 2016, @02:25PM
I suspect the solution involves asking the gods themselves about what they think the other gods would say.
Sounds like that requires some luck. If A and B are True and False, asking either of them what C will say will...cause a crash or something? And asking C what A or B will say produces a random answer.
I'm not convinced it's fair to call this "the hardest logic puzzle." You could take any logic puzzle of similar form, determine the minimum number of questions necessary to solve it, then say you're only allowed to ask n - 1 questions, which it kind of sounds like this thing is.
Flashbacks to Discrete Math and that damn Monty Hall Problem :P
"Is that really true?" "I just spent the last hour telling you to think for yourself! Didn't you hear anything I said?"
(Score: 1, Insightful) by Anonymous Coward on Sunday October 23 2016, @06:54PM
Ask each one in turn: "Will you give me the answer to this problem in a way that I unambiguously and easily know it is the correct answer xor answer this question with whatever means no?". The one who answers truthfully will be forced violate the constrains of the problem and grant you the answer (regardless of his response). You can also add a clause to request infinite happiness or whatever: just "and" it into that the left operand of the xor and the truth god will have to grant it. This uses the same principal as the introduction to the problem, which means it seem obvious and clearly not the hardest logic problem.
You can also attack this problem from another perspective: First prove false equals true by asking all of them a paradox that cannot be answered truthfully: "Is your answer incorrect xor will you answer no?". If you assume the preconditions, and get an answer from each god, one must have answered it truthfully. Then you can use false implies true to prove the answer is anything you want. ( http://www.cut-the-knot.org/do_you_know/falsity.shtml [cut-the-knot.org] )
If you want to make the problem more robust, you can constrain it such that the gods only provide one bit of information, and if doing so would be a paradox, they select it arbitrarily.
If you want the hardest logic problem, it has been proven that there are logic problems that have an answer but can not be solved (this is a consequence of Gödel's incompleteness theorems). Unfortunately its impossible to know which problems they are, but impossible clearly seems like the hardest difficulty level.
(Score: 2) by darkfeline on Sunday October 23 2016, @08:42PM
The solutions don't seem to make sense?
>The first is one of Smullyan’s classic knights and knaves riddles ... knights always tell the truth, knaves always lie, and your task is to find out who’s who. The solution is to ask a question like, “Are you a knight if and only if two plus two is four?”
Knights: T T = T (both predicates are tautologies), knight answers Yes
Knave: F T = F (contradiction, tautologies), Knave answers Yes
You get no information from asking that question.
>In the second puzzle, you know you’re asking a knight—but he only responds with “da” and “ja.” The strategy here is a variant of that in the first puzzle: You ask, “Does ‘da’ mean ‘yes’ if and only if two plus two equals four?”
Da: T T = T, answers Yes
Ja: F T = F, answers Yes
Again, no info.
>Suppose I place three cards in a row in front of you—two aces and a jack—face down. You don’t know how they’re ordered, but I do. You can ask one yes-no question, while pointing at one of the cards. If you happen to point at one of the two aces, I’ll answer the question truthfully, like a knight; if you point at a jack instead, I’ll answer “yes” or “no” at random, like Random. Where will you point, and what will you ask?
>The answer: Point to any card and ask if one of the other cards is an ace.
Ace: T (tautology) answers Yes
Jack: T (tautology) answers Yes or No
If you get a Yes you're fucked, if you get a No (pure luck), you know it's a jack.
Join the SDF Public Access UNIX System today!
(Score: 2) by mhajicek on Sunday October 23 2016, @09:35PM
If the three are gods, they may answer your insolence with a lightening bolt to the face.
The spacelike surfaces of time foliations can have a cusp at the surface of discontinuity. - P. Hajicek
(Score: 2) by FatPhil on Sunday October 23 2016, @09:39PM
The knight is a knight even if 2+2!=4, so he answers No.
Isn't "does 2+2=4?" a better question? Knights answer "yes", knaves answer "no".
Great minds discuss ideas; average minds discuss events; small minds discuss people; the smallest discuss themselves
(Score: 2) by aristarchus on Sunday October 23 2016, @11:46PM
The classic question, by Kaspar Hauser in The Enigma of Kaspar Hauser (German: Jeder für sich und Gott gegen alle; lit. Every Man for Himself and God Against All), by Werner Herzog, is "Are you a tree frog?" Knights usually answer "nein". Knaves answer "ja", and the jig is up!
Citation: https://en.wikipedia.org/wiki/The_Enigma_of_Kaspar_Hauser [wikipedia.org]
(Score: 0) by Anonymous Coward on Monday October 24 2016, @04:55PM
What happens if you ask "how many tree frogs are you?" Nein!
(Score: 2) by kazzie on Monday October 24 2016, @06:11PM
In that case, the knight will say “ni”!
(Score: 2) by FatPhil on Sunday October 23 2016, @09:42PM
Great minds discuss ideas; average minds discuss events; small minds discuss people; the smallest discuss themselves
(Score: 3, Informative) by AthanasiusKircher on Monday October 24 2016, @03:00AM
The "two plus two equals four" stuff is the article's attempt to try to "paraphrase" the actual published solution to the problem (from 1996), but it doesn't make a lot of sense the way it's phrased. If you really want to understand the solutions, look them up (or solve the puzzle yourself) -- the phrasing TFA is just muddled and I'm not sure it actually is doing what the author thinks it is. (In fact, I'm pretty sure TFA is pretty confused about how the first two puzzles actually work.)
As for the last problem, the quoted solution is correct -- I think you missed the detail that you're pointing at a different card from the one you're asking about. Imagine there are three cards, and I point to the middle one while asking "Is the card on the right an Ace?" My behavior is to choose the right card if you say "Yes" and the left card if you say "No."
Why? Well, if the middle card is an Ace, then you'll answer truthfully. So if you say "Yes" I know the card on the right is an Ace and thus I choose it. If the card on the right is a Jack, you'll say "No," so I'll go with the card on the left.
If, on the other hand, the middle card is a Jack, you'll answer randomly. But in that case your answer doesn't matter, since the Jack's in the middle and the two outer cards are Aces. Thus, whether I go with the card on the right or the left, I will definitely get an Ace.
(Score: 2) by darkfeline on Monday October 24 2016, @03:41AM
Thanks for the clarification. The article was unclear about the goal of the last problem, which I assumed was to identify what all the cards are. It sounds like this is impossible, since in the proposed solution, you can only guarantee picking one ace, and cannot guarantee identifying all three cards/the jack.
Join the SDF Public Access UNIX System today!
(Score: 2) by AthanasiusKircher on Monday October 24 2016, @05:31AM
Yes, I now realize that TFA is vague on that point too. In general, it's a really bad presentation that basically completely rips off the original 1996 article but manages to screw stuff up and be vague so that the material is completely unclear.
(Score: 2) by shortscreen on Sunday October 23 2016, @08:46PM
does posting a solution earn one a kiss from martyb or janrinok?
(Score: 2) by martyb on Monday October 24 2016, @08:42AM
Sure! [wikipedia.org]
Wit is intellect, dancing.
(Score: 2) by janrinok on Monday October 24 2016, @09:20AM
(Score: 2) by The Mighty Buzzard on Sunday October 23 2016, @09:01PM
I'll admit it took me a few minutes but I've run into harder logic problems coding this site. I'm not spilling the beans and depriving the rest of you of the fun of figuring it out though.
My rights don't end where your fear begins.
(Score: 1) by Grey on Monday October 24 2016, @02:39AM
I spent a lot of time thinking about this problem a year or two back. It's fun because one can, meaningfully, think about what it means to say that it takes 2.5 bits of information to answer a question (that's a random non-integer-- not directly related to the problem). I think the problem might be *slightly* overspecified (by which I mean there are 6 possible ways to assign identity to the individual Gods, but 8 possible answers to 3 yes/no questions)-- so I suspect that there is a "harder" problem with a similar scope, although I don't know what that problem happens to be.
In any event, I also found the question particularly interesting because it highlights the difference between randomly choosing to answer truthfully or falsely against just choosing a random answer (and those two situations are *not* the same). One Hint: It's possible to use one yes/no question to figure out whether ja or da is "yes" or "no", but that "burns up" too many bits and doesn't leave enough to resolve the possible identity-configurations. Hence the proper answer will NOT reveal the meaning of ja and da.
(Score: -1, Troll) by Anonymous Coward on Monday October 24 2016, @02:54AM
That's why you never get dates. Nerds - social morons.
(Score: 3, Interesting) by Jiro on Monday October 24 2016, @05:42AM
"If I asked you X, would you say 'da'?" will produce the answer "da" if the answer to X is "yes" and "ja" if the answer is "no", regardless of whether the person is True or False and regardless of whether "da" means "yes" and "ja" means "no" or vice versa.
If you modify this to "If I asked you X and you responded using the truthteller status you used in answering this question, it will also work on Random. That lets you solve the puzzle in three questions since you have 3 bits of information for 6 possibilities.
You can actually solve it in 2 questions. Since Random always speaks truly or falsely, there are questions which he cannot answer (such as "is your answer to this question a lie?"). Your question would simply be "If I am Random, then (unanswerable question), else (question from the previous paragraph)", appropriately rephrased to be a question.
I'm sure there is an answer that is simpler, but less systematic.
(Score: 1) by jsdfk on Monday October 24 2016, @11:50AM
Disclaimer : could be wrong
We have 3 gods T (True), F (False) and R (Random).
As we don't know which god is which, let's assign identifiers to them : A, B and C.
The gods answer in their own language, where ja and da mean yes and no, not necessarily in this order.
Problem overview
----------------
We have to find which god is which. We have to find a mapping between
( A, B, C ) and ( T, F, R ). We have the following 6 options :
(I)
A B C
T F R 1
T R F 2
F T R 3
F R T 4
R T F 5
R F T 6
We can ask the gods 3 questions, on each we get an answer ja or da.
This means that we can get in total 8 different sets of answers ( 2^3 = 8, ja/da 3 times ).
We also don't know the mapping between ja / da and yes / no :
(II)
1) da = yes, ja = no
2) da = no, ja = yes
From this alone we can see that if we want to determine the mapping ja/da to yes/no
as well as the mapping (I) (6x2=12 possibilities), we don't have enough questions
(with 3 questions we can distinguish between 8 possibilities).
Therefore our solution will not include the mapping ja/da to yes/no.
Part 1 : eliminating da/ja mapping problem
------------------------------------------
Let's suppose we ask one god X a question of type
( Q if and only if "ja" means "yes" in your language ).
The result, presuming the god will answer truthfully :
Q ("da=="yes") (Q iff "da"=="yes") word we hear
T T T da
T F F da
F T T ja
F F T ja
iff means if and only if, Q is an arbitrary question.
Therefore by asking the god (Q iff da==yes) we hear da exactly when Q is true.
Using this we can eliminate the problem of not knowing the mapping (II),
simply by asking (Q iff "da"=="yes) instead of just asking Q.
Part 2 : deducing truth from an answer by a T/F god
---------------------------------------------------
If we are talking to a god that is either T or F, how do we learn the truth ?
By asking ( Q iff (you are T god) ) we get the following truth table :
Q (you are T) (Q iff (you are T)) (answer we hear)
T T T T (tells the truth)
T F F T (lies)
F T F F (truthfully)
F F T F (lies)
Therefore by asking (Q iff (you are T)) we can determine the truth of the statement Q.
In combination with part 1, this means that we will have to ask :
( Q if and only if you are T ) if and only if "da" means "yes"
and will hear "da" from a god that is T or F exactly when our question Q is true.
Part 3 : Solution
-----------------
Lets define our question Q'( i, j, k, ..., n ) as :
Q'( i, j, ..., n ) :
is it true that at leas one of the following statements is true :
- You identities are as describe in table (I), row i
- You identities are as describe in table (I), row j
- ...
- You identities are as describe in table (I), row n
and Q( i, j, ..., n ) as :
Q( i, j, ..., n ) = ( Q' iff you are T ) iff ( "da" == "yes" )
By asking a T/F god a question Q( i, j, k ) we will therefore determine the following :
- if he answers "da", we will know that only possibilities (i,j and k) in our table are possible
- if he answers "ja", we will know that possibilities (i,j and k) are not possible
Solution :
Ask god A question Q( 1, 3, 5 ).
If he answers "da", we know that only options 1, 3, and 5 are possible, __if he is a T/F god__.
In that case god B can not be R. If god A is R, then his answer doesn't matter, and god B can not be R as well.
We ask god B question Q( 1, 2, 3 ) :
- answers "da" : ask god B question Q( 1 ) :
- answers "da" : option 1 in table
- answers "ja" : option 3 in table
- answers "ja" : ask god B question Q( 5 ) :
- answers "da" : option 5 in table
- answers "ja" : option 6 in table
If A answers with "ja" in the first case, proceed similarly by asking C similar questions.
(Exercise left to the reader)
(Score: 2) by Bot on Tuesday October 25 2016, @11:41AM
> His statement was: "You'll give me neither your autograph nor a kiss."
If you correctly consider the value of true and false as external to the logic system, being it meta information, you can give one autograph. You just optionally specify that you gave it because you wanted to make the statement false (and so no further autograph will be given because of the truth of the statement itself) or because you decided not to give the autograph, so you give it because of the truth of the statement itself. You just distinguish the reason for it.
If the three gods do the same, I guess the logic puzzle solver is fucked.
So a good way to get a kiss would have been to substitute kiss for autograph, but then it would be obvious what would get forced.
Besides, it is not a hard logic puzzle. It is just a complicated one.
If you want something arguably hard, because there is no table of possibilities to solve for a solution, think about this:
A beggar is wandering in the city, hungry. He gets drawn to the delicious smell of cooked meat coming from a house and approaches it. Knocks and the owner lets him in the kitchen.
The beggar is about to talk but from a nearby open door, obscured by a tent, the hee haws of a donkey interrupt him. The owner shouts "cut it out!". The sounds ceases.
The beggar, with the mouth watering from the smell of food, says "sir, i am hungry and..."
From the nearby room it can be heard the cluck cluck of chickens.
I guess you want food, says the owner. Well if you do me a favor...
From the nearby room comes the baa of a goat.
Shush! says the owner. And tells the beggar: "Fuffy is hungry, there is an animal shop round the corner, ask them to deliver me food for my pet Fuffy, Fuffy is an..."
I know what kind of animal Fuffy is, obviously, replied the beggar.
spoiler
spoiler
spoiler
spoiler
solution, fuffy is a parrot, or one of those crows that can imitate other animals sounds. There could not be those animals they heard kept in a room, also their smell would overpower the smell of food. The owner interacts with the sound so it is not a record or radio.
Account abandoned.