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Topic: NEW PROBLEM: The Gods of Gibberland (Read 18330 times) |
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Rupert
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Re: NEW PROBLEM: The Gods of Gibberland
« Reply #75 on: Aug 17th, 2002, 10:30pm » |
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on Aug 17th, 2002, 10:13pm, Eric Yeh wrote:The "problem" with stating the problem that way is that it reduces the search space too much, thereby actually making the problem easier to solve.
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You are right. If at all, it should be a 'second round' add-on.
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Eric Yeh
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Re: NEW PROBLEM: The Gods of Gibberland
« Reply #76 on: Aug 18th, 2002, 8:15am » |
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Glad you agree -- didn't want to offend you!! `:)
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Jabberwock
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Re: NEW PROBLEM: The Gods of Gibberland
« Reply #77 on: Aug 29th, 2002, 8:32am » |
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Finally!!!!
I've been working on this problem on and off for the last few weeks and finally solved it. Thank you for such a challenge! I ended up with roughly the same solution as Jonathan, although I think I took a longer path to it. 
I started of with compound questions, hoping that I could extract the language by the end, but that was obviously a dead end. I then realized that I would need to differentiate between the answers (like Jonathan did), but I was still thinking of compound questions, like "Is T < F AND are you the Knexus...". After a lot of truth tables I realized that simpler could be better. 
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Eric Yeh
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Re: NEW PROBLEM: The Gods of Gibberland
« Reply #78 on: Aug 29th, 2002, 8:42am » |
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Congratulations Jaberwock! Glad you enjoyed the puzzle!!! And yay, another newly registered user honoring my thread with his first post.
By the way, don't you want another b in your name?? 
Best,
Eric
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Jabberwock
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Re: NEW PROBLEM: The Gods of Gibberland
« Reply #79 on: Aug 29th, 2002, 8:49am » |
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Grr... should have payed more attention before I created that. Now it should show up correctly but I have to remember to login with the misspelled version.  But anyway, I'm gladd to finally be a member after the past month of lurking.
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Eric Yeh
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Re: NEW PROBLEM: The Gods of Gibberland
« Reply #80 on: Aug 29th, 2002, 8:53am » |
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Heh -- gd for you. I like your pic -- is that your own? I don't remember seeing it as a choice.
Have you looked at my other two currently posted problems?
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Jonathan_the_Red
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Re: NEW PROBLEM: The Gods of Gibberland
« Reply #81 on: Sep 10th, 2002, 2:19pm » |
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Hey, Eric, do you mind if I share this puzzle with some Microsoft folks? Giving full credit where it is due, of course.
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My arcade cabinet
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Eric Yeh
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Re: NEW PROBLEM: The Gods of Gibberland
« Reply #82 on: Sep 10th, 2002, 2:58pm » |
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That would be fine -- I appreciate your asking! So you work at MSFT eh?
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Eric Yeh
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Re: NEW PROBLEM: The Gods of Gibberland
« Reply #83 on: Oct 12th, 2002, 4:24pm » |
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So Jon, following up: what'd the MSFT ppl think?? How's the puzzle comp?
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Jonathan_the_Red
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Re: NEW PROBLEM: The Gods of Gibberland
« Reply #84 on: Oct 12th, 2002, 8:46pm » |
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To tell you the truth, Eric, nobody responded when I sent the puzzle to the Puzzle Hunt mailing list... although at least one person, Garzahd, was drawn to this group because of it. At least a couple of my personal acquaintances are working on the puzzle right now.
The Puzzle Hunt was a rousing success... my team finished a semi-respectable seventh out of about 45. Next year we'll do better. (We would have placed higher, except we solved a critical meta-puzzle with less than two minutes to go in the hunt and didn't have time to submit our answer.)
The organizers have asked that we not post the puzzles outside of Microsoft until some copyright issues are cleared up... if/when they clear us, I'll put them up somewhere they're accessible to this group. The puzzles were (IMHO) of mixed quality... some of them were fairly uninspired, but others were gold. Many of them cannot be solved without access to internal Microsoft sites or the Microsoft campus itself, and others require physical items (decks of cards, lengths of cord) that were provided to us.
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Eric Yeh
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Re: NEW PROBLEM: The Gods of Gibberland
« Reply #85 on: Oct 12th, 2002, 10:49pm » |
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Aw, that is too bad.  Well, glad at least some others are working on it.
Congratulations on your "semi-respectable" finish! Sounds like it was a lot of fun. I will look forward to hearing some of these "gold" questions.
Best,
Eric
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carpao
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Re: NEW PROBLEM: The Gods of Gibberland
« Reply #86 on: Jun 22nd, 2004, 3:10pm » |
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on Aug 16th, 2002, 6:43pm, Jonathan_the_Red wrote:DO NOT HIGHLIGHT IF YOU DON'T WANT TO SEE A SOLUTION DO NOT HIGHLIGHT IF YOU DON'T WANT TO SEE A SOLUTION DO NOT HIGHLIGHT IF YOU DON'T WANT TO SEE A SOLUTION DO NOT HIGHLIGHT IF YOU DON'T WANT TO SEE A SOLUTION DO NOT HIGHLIGHT IF YOU DON'T WANT TO SEE A SOLUTION DO NOT HIGHLIGHT IF YOU DON'T WANT TO SEE A SOLUTION DO NOT HIGHLIGHT IF YOU DON'T WANT TO SEE A SOLUTION DO NOT HIGHLIGHT IF YOU DON'T WANT TO SEE A SOLUTION DO NOT HIGHLIGHT IF YOU DON'T WANT TO SEE A SOLUTION DO NOT HIGHLIGHT IF YOU DON'T WANT TO SEE A SOLUTION DO NOT HIGHLIGHT IF YOU DON'T WANT TO SEE A SOLUTION DO NOT HIGHLIGHT IF YOU DON'T WANT TO SEE A SOLUTION DO NOT HIGHLIGHT IF YOU DON'T WANT TO SEE A SOLUTION DO NOT HIGHLIGHT IF YOU DON'T WANT TO SEE A SOLUTION
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Ask God A: "Does the word for 'yes' come alphabetically before the word for 'no'?"
GibberKnight will say whichever answer word comes alphabetically first. GibberKnave will say whichever answer word comes alphabetically second. GibberKnexus will say whichever answer word means 'yes'.
Ask God A: "Does the word for 'no' come alphabetically before the word for 'yes'?"
If the answers to the two questions are the same, God A is GibberKnexus, and his answer means 'yes'. Ask God B: "Is 2+2 equal to 4?" If his answer is the same as God A's answers, he's the Knight, otherwise he's the Knave.
If the answers to the two questions differ and the answer to question 1 precedes the answer to question 2 alphabetically, he's a Knight. If the answer to question 2 precedes the answer to question 1, he's a knave.
Either way, you can use the iff trick combined with the "what would you say if I asked you..." trick to determine which of the other Gods is which.
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I'm missing the last passage...
If we had two different answer at the first two question I agree that we can understand who is the questioned god by examine the order...
but we have no indication of what is the word for "yes" and what is the word for "no"...
So finally how we can understand the last two gods?
If we make a question where both must answer the same... it is clear that we cannot distinguish them...
but if we make a question where they must answer differently... we (not knowing what is yes and what is no) cannot distinguisj again...
probably we have to introduce in the iff clause a dependency on a binding of 'yes' with one of the "heard words"...
but could someone help me in understanding the last question?
thanks
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Three Hands
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Re: NEW PROBLEM: The Gods of Gibberland
« Reply #87 on: Jun 22nd, 2004, 3:35pm » |
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The cunning part is that, through knowing who the god you are questioning is, you can then remember the answers given in order to say what the terms for "yes" and "no" are (except in the case of GibberKnexus, but then you only know what the term for "yes" is, and so could presumably deduce what "no" is). If you have worked out that GibberKnight answered, then the first answer means "yes" and the second answer means "no". If you were asking GibberKnave, then the first answer means "no" and the second answer means "yes". Therefore, assuming you remember which word is which, you can translate the subsequent answers.
Oh, and belated congratulations to Jonathan - only just seen this thread, and having seen the answer you reached, I can only say it's an answer I would have struggled to reach (if I reached it at all!!!!)
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Leo Broukhis
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Re: NEW PROBLEM: The Gods of Gibberland
« Reply #88 on: Jun 22nd, 2004, 7:27pm » |
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This answer is very hard to reach indeed, because the ability of the visitor to perform a lexicographic comparison (whose result matches the gods' result) does not follow from the problem statement. The only ability that does naturally follow is the ability to perform an equality comparison.
What if the gods understand English but respond in Chinese?
As the trick is in asking a question about a property of the responses that is "computable" by the visitor, what is such a property of an audio sample?
The questions about a totalistic property (duration, average frequency, etc.) are out, because the two samples can have equal totalistic properties, but what is the best (simplest) dynamic property?
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| « Last Edit: Jun 22nd, 2004, 8:22pm by Leo Broukhis » |
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Eric Yeh
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Re: NEW PROBLEM: The Gods of Gibberland
« Reply #89 on: Jun 22nd, 2004, 8:20pm » |
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Leonid,
It is true that the precision of Jonathan's "lexicon" solution of yesteryear is slightly debatable. But as it was so close to the originally conceived solution, I had let it pass with hearty congratulations. But perhaps it is finally time to close this minor little hole.
To be more precise, one simply needs to assert that the asker create any total ordering on the set of all possible responses. For example, this may be a function which maps the set of all possible sounds to the real axis. Although there are arbitrarily many ways to create this function -- one of which can be extended by a lexicographic type of argument a la Jonathan's -- my original and still favorite way to conceive of this (which in my mind remains incredibly intuitive and irrefutable) is a function whereby "A > B" iff "I like the sound of A better than the sound of B."
Once you believe that a fixed ordering exists, note that the Gods, being omniscient, know whether A > B or B > A, where A and B are their words for yes and no. Then substitute "A > B" for "A earlier than B" in Jonathan's argument, and you are done. [As before, you need to be sure that the responses of AAA and BBB, if they arise at all, imply the same ordering of gods.]
Hope that solution is satisfactory to all my readers here! Thanks again to everyone for their interest!!!
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BNC
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Re: NEW PROBLEM: The Gods of Gibberland
« Reply #90 on: Jun 22nd, 2004, 10:08pm » |
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Hi Eric,
We hardly see you around -- glad you drop by from time to time!
As for the "like the sound" approach, I'm not sure if it's guaranteed to work. Even assuming that the mapping of all possible sounds to the "like" axis is one to one, the two sounds may be arbitrary close to each other.
So the omniscient gods can tell that "snift" is slightly more likable to you than, say, "snuft". But in your mind, they may be undistinguishable close.
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How about supercalifragilisticexpialidociouspuzzler [Towr, 2007]
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carpao
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Re: NEW PROBLEM: The Gods of Gibberland
« Reply #91 on: Jun 23rd, 2004, 2:52am » |
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on Jun 22nd, 2004, 3:35pm, Three Hands wrote:If you have worked out that GibberKnight answered, then the first answer means "yes" and the second answer means "no". If you were asking GibberKnave, then the first answer means "no" and the second answer means "yes". Therefore, assuming you remember which word is which, you can translate the subsequent answers.
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one moment to think
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| « Last Edit: Jun 23rd, 2004, 2:56am by carpao » |
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carpao
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Re: NEW PROBLEM: The Gods of Gibberland
« Reply #92 on: Jun 23rd, 2004, 3:04am » |
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on Jun 23rd, 2004, 2:52am, carpao wrote:
I don't agree with that...
let me make a counterexample:
if they speak italian yes is "SI" and no is "NO"
now to the question:
does the translation("yes") precedes translation("no")?
the gibberknight answers:
NO
and to the question:
does the translation("no") precedes translation("yes")?
the gibberknight answers:
SI
because the NO precedes SI I understand that it is Gibberknight, but as you can see the first answer is the translation of "no"...
To be complete, let consider the other case:
if the translation of "yes" is "ASI"
now to the question:
does the translation("yes") precedes translation("no")?
the gibberknight answers:
ASI
and to the question:
does the translation("no") precedes translation("yes")?
the gibberknight answers:
NO
this time the first word is the translation of "yes"
(again I can however still identifies the god as GibberKnight from the fact that ASI precedes NO)
So after the two questions I am able to identify the god that I asked, but (if he is not GibberKnexus) I don't know what are the binding from yes and no to their translation
So... what is the solution for teh last question?
BTW if it was true that I had also te binding of the translation the last question is very simple and exactly of the form:
is true equal to false?
or
is true equal to true?
(dependent from who was the the identified god)
so it would not require the "iif" (if and only if) and complicated form proposed in the original solution...
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rmsgrey
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Re: NEW PROBLEM: The Gods of Gibberland
« Reply #93 on: Jun 23rd, 2004, 5:49am » |
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So you've established that the words for yes and no are X and Y (in some order), and that you're talking to someone who is always truthful (or always lies - but you know which)
So you need a question that the (known) truthful deity, A, will answer differently depending on whether B is the liar or the knexus, but the same way regardless of which of X and Y is yes.
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If I were to ask you whether B is the Gibberknexus, would your answer be X?
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Analysis:
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If B is knexus, and X is yes, then A would answer X(yes) to the inner question and so answers X(yes) to the whole question.
If B is knexus and X is no, then A would answer Y(yes) to the inner question, so answers X(no) to the whole question.
If B is not knexus, X yes, then A would answer Y(no) to the inner question, so answers Y(no) to the whole question.
If B is not knexus, X no, then A would answer X(no) to the inner question, so answers Y(yes) to the whole question.
Similarly, if A is known to be the liar, then the same question produces the same answers, for example:
If B is knexus and X is yes, A would falsely answer Y(no) to the inner question, so falsely answers X(yes) to the whole question.
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See the "transylvanian fork in the road" and "another fork in the road" threads for a simpler knight/knave type problem with an unknown language.
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Eric Yeh
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Re: NEW PROBLEM: The Gods of Gibberland
« Reply #94 on: Jun 23rd, 2004, 6:41am » |
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BNC,
Haha thanks -- I still keep watches over the threads I always watched (too lazy to change those settings!); I don't necessarily check all of them, but I definitely read messages for the ones I've created. Not usually a lot of activity though Hahaha.
To address your concern: Yes, clearly there is a requirement that you need to be able to distinguish the answers for yes and no. Beyond that, it is up to you to convince yourself that given any two sounds, you can find a function that totally orders them. A cool result is that you don't actually need to be consistent among different sets of sounds, eg, you dont actually need transitivity. You only need antisymmetry.
Well, at some point the debate becomes semi-philosophical, and I do apologize to you or anyone else who finds this sollution unsatisfying. I toyed with the idea of having the gods speak in strings of English letters etc, but it just made the problem much less believable sounding in a way that, to me, not only detracted from the elegance of the problem statement, but also gave an automatic clue to the solution (though it is far from full!). In the end, I chose the route that I knew would be slightly more controversial in this metaphysical sense, but luckily I have had no challenges till now
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carpao
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Re: NEW PROBLEM: The Gods of Gibberland
« Reply #95 on: Jun 23rd, 2004, 7:15am » |
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on Jun 23rd, 2004, 5:49am, rmsgrey wrote:...
So you need a question that the (known) truthful deity, |
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THANKS A LOT this was the point
I was so stupid that I looked for a question to ask to one of the other two gods...
for Eric... thanks for this beautiful riddle...
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Eric Yeh
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Re: NEW PROBLEM: The Gods of Gibberland
« Reply #96 on: Jun 23rd, 2004, 7:38am » |
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many thanks carpao!!! those little notes really mean a lot to me!!!
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rmsgrey
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Re: NEW PROBLEM: The Gods of Gibberland
« Reply #97 on: Jun 23rd, 2004, 7:43am » |
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If you can't distinguish between "yes" and "no" when you hear them, then you can't get any information at all. So for the problem to be at all solvable, you need to be able to distinguish between the two words, so all you need to be able to do is come up with a system which, given any pair of words orders the pair in the same way each time the same pair come up (regardless of the order in which they appear). You don't even need to know the function explicitly yourself - it just needs to be a reliable "black box" provided the deities omniscience applies to it.
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Stinkbeard
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Re: NEW PROBLEM: The Gods of Gibberland
« Reply #98 on: Nov 12th, 2007, 9:06am » |
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Maybe the gods can answer in musical tones? That seems a very godly way to communicate.
Q1: Is your word for yes a higher pitch than your word for no?
Q2: Is your word for yes a lower pitch than your word for no?
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Tasselfoot
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Re: NEW PROBLEM: The Gods of Gibberland
« Reply #99 on: Mar 24th, 2008, 3:46pm » |
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I posted a new thread for this, so my apologies if bumping this in addition is frowned apon.
I am curious as to 3 questions to ask based upon a 3rd deity that responds randomly instead of XOR.
I assume that it is all VERY similar, but frankly, trying to comprehend the responses of the deities, even on paper, gives me a massive headache.
So any assistance would be most appreciated, as this is a problem posed to a group of us on another site.
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