This is a good puzzle - except I can't solve it!

Thanee said:
If you cannot solve this (which is really not so hard), you should not even look at the advanced version of this puzzle.

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.

;)

Bye
Thanee

Do all the gods speak the same language? Or could each god's translation of yes and no be different?
 

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Thanee said:
If you cannot solve this (which is really not so hard), you should not even look at the advanced version of this puzzle.

I've always heard a slightly different form of the puzzle:
There are three omniscient gods sitting in a chamber: GibberKnight, GibberKnave, and GibberKnexus, the gods of the knights, knaves, and knexuses of Gibberland. Knights always answer the truth, knaves always lie, and knexuses always answer the XOR of what the knight and knave would answer.

Unfortunately, the language spoken in Gibberland is so unintelligible that not only do you not know which words correspond to "yes" and "no", but you don't even know what the two words that represent them are! All you know is that there is only one word for each.

With only three questions, determine which god is which.

Note 1: What follows are standard rules that are generally assumed unless otherwise noted. The gods only answer yes/no questions. Each god answers in the single word of their language as appropriate to the question; i.e. each god always gives one of only two possible responses, one affirmative and one negative (e.g. they would always answer "Yes" rather than "That would be true"). Each question asked must be addressed to a single specific god; asking one question to all the gods would constitute three questions. Asking a single god multiple questions is permissible. The question you choose to ask and the god you choose to address may be dynamically chosen based on the answers to previous questions. No self-referential questions (e.g. "is this question true iff ...").

Note 2: Because of possible loop conflicts, you may not ask any questions regarding how a knexus would answer.

The difference, I suppose, being that the knexus's behavior is better defined than a random yes/no.
 
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LavosBacons said:
I've always heard a slightly different form of the puzzle:


The difference, I suppose, being that the knexus's behavior is better defined than a random yes/no.

Well, first thing that popped into my head. I'm not sure if this is rule-breaking, since you said it was implied?

First ask: What would you say if I asked you if you were the Knexus?
Knight will say No.
Knave will say Yes.
Knexus will not be able to answer. It's non-deterministic

If the first two say something, then the last one is the Knexus.
Ask: Are you the Knexus?
The Knight's answer would have been No, while the Knave's would have been yes, making the Knexus's answer yes. So whoever answered the same as the Knexus is the Knave.

If only one of the first ones says something, use the new question on the one that did not say anything (who is the Knexus). If they answered the same as the first one, the first one was the Knave, if he didn't, the unquestioned one is the Knave.
 

Definitely an oldie but a goodie.

By far, my favorite incarnation of this puzzle is from "The 10th Kingdom."

Basically, father, daughter and her boyfriend just get done sneaking into the basement of the castle. They had to sneak past guards, swim underwater for a few minutes and go through all kinds of crud to get there.

Anyway, as soon as they emerge from the water, they find two doors. A bullfrog is on a pedestal on the opposite end of the room. He says something to the effect of "One door will lead to certain death; the other to what you seek."

The daughter and boyfriend start discussing the riddle. The father, short tempered at this point, says "Enough of this," picks up the bullfrog "Wait! What are you doing?! This is not the way to..." and opens up one of the doors, THROWS THE BULLFROG IN IT and slams the door. A few seconds later an explosion is heard behind the door.

"I guess we use the other door then." :lol:
 
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Ah, yes, Labyrinth... I liked that movie... all except for the music which I found rather jarring given the context... but then I've never been a big David Bowie fan. This is a classic puzzle, and it reminds me of a wonderful short story by Frank Stockton that we read in English class a long, long time ago... I've quoted it here after having found it online (on the theory that this would fall into the "Fair Use" clause of copywrite law - if not I apologize to the moderators, et. al. for its inappropriate usage)... I recall we read a sequel to it written by the author after much harranguing from fans wanting to know the answer. The sequel was three men from a far off land who only heard the story as it is told here and traveled far and wide to discover the answer. In response to their question they were told another story, which ended much as the first did, and were told that if they got the answer to the second right, they would be told the answer to the first... :p

The Lady Or The Tiger?

In the very olden time there lived a semi-barbaric king, whose ideas, though somewhat polished and sharpened by the progressiveness of distant Latin neighbors, were still large, florid, and untrammeled, as became the half of him which was barbaric. He was a man of exuberant fancy, and, withal, of an authority so irresistible that, at his will, he turned his varied fancies into facts. He was greatly given to self-communing, and, when he and himself agreed upon anything, the thing was done. When every member of his domestic and political systems moved smoothly in its appointed course, his nature was bland and genial; but, whenever there was a little hitch, and some of his orbs got out of their orbits, he was blander and more genial still, for nothing pleased him so much as to make the crooked straight and crush down uneven places.
Among the borrowed notions by which his barbarism had become semified was that of the public arena, in which, by exhibitions of manly and beastly valor, the minds of his subjects were refined and cultured.
But even here the exuberant and barbaric fancy asserted itself. The arena of the king was built, not to give the people an opportunity of hearing the rhapsodies of dying gladiators, nor to enable them to view the inevitable conclusion of a conflict between religious opinions and hungry jaws, but for purposes far better adapted to widen and develop the mental energies of the people. This vast amphitheater, with its encircling galleries, its mysterious vaults, and its unseen passages, was an agent of poetic justice, in which crime was punished, or virtue rewarded, by the decrees of an impartial and incorruptible chance.
When a subject was accused of a crime of sufficient importance to interest the king, public notice was given that on an appointed day the fate of the accused person would be decided in the king's arena, a structure which well deserved its name, for, although its form and plan were borrowed from afar, its purpose emanated solely from the brain of this man, who, every barleycorn a king, knew no tradition to which he owed more allegiance than pleased his fancy, and who ingrafted on every adopted form of human thought and action the rich growth of his barbaric idealism.
When all the people had assembled in the galleries, and the king, surrounded by his court, sat high up on his throne of royal state on one side of the arena, he gave a signal, a door beneath him opened, and the accused subject stepped out into the amphitheater. Directly opposite him, on the other side of the enclosed space, were two doors, exactly alike and side by side. It was the duty and the privilege of the person on trial to walk directly to these doors and open one of them. He could open either door he pleased; he was subject to no guidance or influence but that of the aforementioned impartial and incorruptible chance. If he opened the one, there came out of it a hungry tiger, the fiercest and most cruel that could be procured, which immediately sprang upon him and tore him to pieces as a punishment for his guilt. The moment that the case of the criminal was thus decided, doleful iron bells were clanged, great wails went up from the hired mourners posted on the outer rim of the arena, and the vast audience, with bowed heads and downcast hearts, wended slowly their homeward way, mourning greatly that one so young and fair, or so old and respected, should have merited so dire a fate.
But, if the accused person opened the other door, there came forth from it a lady, the most suitable to his years and station that his majesty could select among his fair subjects, and to this lady he was immediately married, as a reward of his innocence. It mattered not that he might already possess a wife and family, or that his affections might be engaged upon an object of his own selection; the king allowed no such subordinate arrangements to interfere with his great scheme of retribution and reward. The exercises, as in the other instance, took place immediately, and in the arena. Another door opened beneath the king, and a priest, followed by a band of choristers, and dancing maidens blowing joyous airs on golden horns and treading an epithalamic measure, advanced to where the pair stood, side by side, and the wedding was promptly and cheerily solemnized. Then the gay brass bells rang forth their merry peals, the people shouted glad hurrahs, and the innocent man, preceded by children strewing flowers on his path, led his bride to his home.
This was the king's semi-barbaric method of administering justice. Its perfect fairness is obvious. The criminal could not know out of which door would come the lady; he opened either he pleased, without having the slightest idea whether, in the next instant, he was to be devoured or married. On some occasions the tiger came out of one door, and on some out of the other. The decisions of this tribunal were not only fair, they were positively determinate: the accused person was instantly punished if he found himself guilty, and, if innocent, he was rewarded on the spot, whether he liked it or not. There was no escape from the judgments of the king's arena.
The institution was a very popular one. When the people gathered together on one of the great trial days, they never knew whether they were to witness a bloody slaughter or a hilarious wedding. This element of uncertainty lent an interest to the occasion which it could not otherwise have attained. Thus, the masses were entertained and pleased, and the thinking part of the community could bring no charge of unfairness against this plan, for did not the accused person have the whole matter in his own hands?
This semi-barbaric king had a daughter as blooming as his most florid fancies, and with a soul as fervent and imperious as his own. As is usual in such cases, she was the apple of his eye, and was loved by him above all humanity. Among his courtiers was a young man of that fineness of blood and lowness of station common to the conventional heroes of romance who love royal maidens. This royal maiden was well satisfied with her lover, for he was handsome and brave to a degree unsurpassed in all this kingdom, and she loved him with an ardor that had enough of barbarism in it to make it exceedingly warm and strong. This love affair moved on happily for many months, until one day the king happened to discover its existence. He did not hesitate nor waver in regard to his duty in the premises. The youth was immediately cast into prison, and a day was appointed for his trial in the king's arena. This, of course, was an especially important occasion, and his majesty, as well as all the people, was greatly interested in the workings and development of this trial. Never before had such a case occurred; never before had a subject dared to love the daughter of the king. In after years such things became commonplace enough, but then they were in no slight degree novel and startling.
The tiger-cages of the kingdom were searched for the most savage and relentless beasts, from which the fiercest monster might be selected for the arena; and the ranks of maiden youth and beauty throughout the land were carefully surveyed by competent judges in order that the young man might have a fitting bride in case fate did not determine for him a different destiny. Of course, everybody knew that the deed with which the accused was charged had been done. He had loved the princess, and neither he, she, nor any one else, thought of denying the fact; but the king would not think of allowing any fact of this kind to interfere with the workings of the tribunal, in which he took such great delight and satisfaction. No matter how the affair turned out, the youth would be disposed of, and the king would take an aesthetic pleasure in watching the course of events, which would determine whether or not the young man had done wrong in allowing himself to love the princess.
The appointed day arrived. From far and near the people gathered, and thronged the great galleries of the arena, and crowds, unable to gain admittance, massed themselves against its outside walls. The king and his court were in their places, opposite the twin doors, those fateful portals, so terrible in their similarity.
All was ready. The signal was given. A door beneath the royal party opened, and the lover of the princess walked into the arena. Tall, beautiful, fair, his appearance was greeted with a low hum of admiration and anxiety. Half the audience had not known so grand a youth had lived among them. No wonder the princess loved him! What a terrible thing for him to be there!
As the youth advanced into the arena he turned, as the custom was, to bow to the king, but he did not think at all of that royal personage. His eyes were fixed upon the princess, who sat to the right of her father. Had it not been for the moiety of barbarism in her nature it is probable that lady would not have been there, but her intense and fervid soul would not allow her to be absent on an occasion in which she was so terribly interested. From the moment that the decree had gone forth that her lover should decide his fate in the king's arena, she had thought of nothing, night or day, but this great event and the various subjects connected with it. Possessed of more power, influence, and force of character than any one who had ever before been interested in such a case, she had done what no other person had done - she had possessed herself of the secret of the doors. She knew in which of the two rooms, that lay behind those doors, stood the cage of the tiger, with its open front, and in which waited the lady. Through these thick doors, heavily curtained with skins on the inside, it was impossible that any noise or suggestion should come from within to the person who should approach to raise the latch of one of them. But gold, and the power of a woman's will, had brought the secret to the princess.
And not only did she know in which room stood the lady ready to emerge, all blushing and radiant, should her door be opened, but she knew who the lady was. It was one of the fairest and loveliest of the damsels of the court who had been selected as the reward of the accused youth, should he be proved innocent of the crime of aspiring to one so far above him; and the princess hated her. Often had she seen, or imagined that she had seen, this fair creature throwing glances of admiration upon the person of her lover, and sometimes she thought these glances were perceived, and even returned. Now and then she had seen them talking together; it was but for a moment or two, but much can be said in a brief space; it may have been on most unimportant topics, but how could she know that? The girl was lovely, but she had dared to raise her eyes to the loved one of the princess; and, with all the intensity of the savage blood transmitted to her through long lines of wholly barbaric ancestors, she hated the woman who blushed and trembled behind that silent door.
When her lover turned and looked at her, and his eye met hers as she sat there, paler and whiter than any one in the vast ocean of anxious faces about her, he saw, by that power of quick perception which is given to those whose souls are one, that she knew behind which door crouched the tiger, and behind which stood the lady. He had expected her to know it. He understood her nature, and his soul was assured that she would never rest until she had made plain to herself this thing, hidden to all other lookers-on, even to the king. The only hope for the youth in which there was any element of certainty was based upon the success of the princess in discovering this mystery; and the moment he looked upon her, he saw she had succeeded, as in his soul he knew she would succeed.
Then it was that his quick and anxious glance asked the question: "Which?" It was as plain to her as if he shouted it from where he stood. There was not an instant to be lost. The question was asked in a flash; it must be answered in another.
Her right arm lay on the cushioned parapet before her. She raised her hand, and made a slight, quick movement toward the right. No one but her lover saw her. Every eye but his was fixed on the man in the arena.
He turned, and with a firm and rapid step he walked across the empty space. Every heart stopped beating, every breath was held, every eye was fixed immovably upon that man. Without the slightest hesitation, he went to the door on the right, and opened it.
Now, the point of the story is this: Did the tiger come out of that door, or did the lady ?
The more we reflect upon this question, the harder it is to answer. It involves a study of the human heart which leads us through devious mazes of passion, out of which it is difficult to find our way. Think of it, fair reader, not as if the decision of the question depended upon yourself, but upon that hot-blooded, semi-barbaric princess, her soul at a white heat beneath the combined fires of despair and jealousy. She had lost him, but who should have him?
How often, in her waking hours and in her dreams, had she started in wild horror, and covered her face with her hands as she thought of her lover opening the door on the other side of which waited the cruel fangs of the tiger!
But how much oftener had she seen him at the other door! How in her grievous reveries had she gnashed her teeth, and torn her hair, when she saw his start of rapturous delight as he opened the door of the lady! How her soul had burned in agony when she had seen him rush to meet that woman, with her flushing cheek and sparkling eye of triumph; when she had seen him lead her forth, his whole frame kindled with the joy of recovered life; when she had heard the glad shouts from the multitude, and the wild ringing of the happy bells; when she had seen the priest, with his joyous followers, advance to the couple, and make them man and wife before her very eyes; and when she had seen them walk away together upon their path of flowers, followed by the tremendous shouts of the hilarious multitude, in which her one despairing shriek was lost and drowned!
Would it not be better for him to die at once, and go to wait for her in the blessed regions of semi-barbaric futurity?
And yet, that awful tiger, those shrieks, that blood!
Her decision had been indicated in an instant, but it had been made after days and nights of anguished deliberation. She had known she would be asked, she had decided what she would answer, and, without the slightest hesitation, she had moved her hand to the right.
The question of her decision is one not to be lightly considered, and it is not for me to presume to set myself up as the one person able to answer it. And so I leave it with all of you: Which came out of the opened door - the lady, or the tiger?
 
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Thanee said:
If you cannot solve this (which is really not so hard), you should not even look at the advanced version of this puzzle.<snip>

I found a book of logic riddles in the library (called "What´s the name of this book?" or something) filled with that kind of head-exploding problems, some of them of that kind but even more difficult. Some of them dealt with vampires (who always lie) and humans (who always tell the truth), but some of them are insane and think they are of the opposite kind. More, they speak the same language of "da" and "ja". Interestingly, at the end there was a single sentence X that added to any question (in the form of "is X equivalent to so-and-so?") that always forced any kind of vampire or human to tell the truth.

Anyway, my favourite riddle is this: In a monastery were 60 monks live (every one of them, thanks to their mental training, can perform astonishingly quick logical calculations), one night a novice sneaks into the cells of seven of them and paints a blue dot in their forehead. In the morning, the monks see blue dots in some foreheads, but since there are no mirrors in the monastery and they have a vow of silence, nobody can know if they have a dot themselves. (thus, the monks with no dots can see all the seven dots and those with a dot can only see six)

The abbot (who can speak) notices the agitation and says: "I´ll chime this bell, and every time I do that, whoever can deduct he has a dot, will raise his hand."

What happens then?

Hint 1:
When the abbot chimes the bell the seventh time, all the dotted monks raise their hands

Hint 2:
Start with a simpler problem. What if there is only one dot? and then two...?
 


Someone said:
The abbot (who can speak) notices the agitation and says: "I´ll chime this bell, and every time I do that, whoever can deduct he has a dot, will raise his hand."

What happens then?

Heh. The hints help.

Morris the Monk has a dot.

If there is only one dot, then Morris can see no dots. He deduces that there must be at least one dot, or the exercise is pointless... therefore it must be on him. When the bell rings, he raises his hand.

If there are two dots, then Morris can see one dot, on Murray the Monk. He knows there is either one dot or two dots, but he doesn't know which. When the bell rings once, he sees that Murray does not raise his hand. Therefore Murray must be seeing the same thing - one dot, and doesn't know if there are one or two. Obviously, then, the dot Murray sees must be on Morris. So when the bell rings the second time, Murray and Morris both raise their hands.

If there are three dots, Morris can see two, on Murray the Monk and Michael the Monk. On the first bell, nobody raises their hand. On the second bell, nobody raises their hand. Morris knows that if there were only two dots, Murray and Michael would have figured this out on the second bell... therefore they must both also be seeing two dots, one of which is on his own head. On the third bell, therefore, Murray, Morris, and Michael all raise their hands.

Etc.

-Hyp.
 

Someone said:
In the morning, the monks see blue dots in some foreheads, but since there are no mirrors in the monastery and they have a vow of silence, nobody can know if they have a dot themselves. (thus, the monks with no dots can see all the seven dots and those with a dot can only see six)

The abbot (who can speak) notices the agitation and says: "I´ll chime this bell, and every time I do that, whoever can deduct he has a dot, will raise his hand."

What happens then?

Easy. At the first time the bell is rung, all seven raise their hands.

C'mon, they're smart, they got to notice all the others staring at their foreheads. :p

(For the real answer, what the smurf said. ;))

Bye
Thanee
 

Yeah, that "Truth guardian/lying guardian" thing does show up a lot. I note that people tend to answer the question in a manner similar to the solution presented by Firelance. That always seemed a bit strange to me, as the question posed to the guardians/gods/what-have-you is not grounded in what the questioner knows to be factual. The problem never stipulates limitations to the guardians' knowledge. My question to the guardians would be more along the lines of "In a base 10 mathematical system, does 2+2 = 4?" You'd only need to ask once. If the guardian responded "yes", he's guarding the heaven door. If "no", he's guarding the hell door and should be avoided. For those of you who object to D&D characters prattling on about base 10 mathematics, substitute "Is the sky blue outside during the daytime" or some such.
 

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