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Topic: NEW PROBLEM: The Gods of Gibberland (Read 18325 times) |
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Rupert
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on Aug 14th, 2002, 9:11pm, Jonathan_the_Red wrote:
BTW, that bastard GibberKnexus completely blows away the iff technique. Take a simple proposition P and ask a Knight or a Knave "does plonk mean 'yes' if and only if P", and the Knight will answer plonk if P is true and blatz otherwise, while the Knave will answer blatz if P is true and plonk otherwise. The Knexus, though, will answer whichever word means yes. No longer does the iff technique break through the language barrier. |
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Good one. I didn't notice that. Well, not good, really. 
What if I asked a question like "If you are Knexus then Qa, otherwise Qb"? Would Knexus answer Qa or Qb? Eric?
(I'm afraid I won't like the answer...  )
Cheers
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Rupert
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Re: NEW PROBLEM: The Gods of Gibberland
« Reply #51 on: Aug 15th, 2002, 4:55am » |
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on Aug 14th, 2002, 8:58pm, Eric Yeh wrote:
Thanks Eric,
Hm. Do you mean there are certain paths where we don't need to find out (this is what I understand Jon meant), or is it generally not necessary? (Don't answer if it gives away too much)
(I'm in Germany)
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Eric Yeh
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Re: Brainstorm
« Reply #52 on: Aug 15th, 2002, 5:25am » |
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on Aug 15th, 2002, 4:25am, Rupert wrote:
If the answer to Q3 is no, you're done. But if it is yes, you still don't know if 'that other guy' is between 'you' and 'that guy' or if he is more reliable than 'you'. -- i.e. the order established by Q2 leaves three 'emtpy spots' from which we would have to decide by just one question.
I hope that I'm wrong here, because that would make it easier, but I'm afraid I' not |
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Ye, I'm afraid I have to agree that if I understand it correctly, I don't see how it bypasses the language barrier.
on Aug 15th, 2002, 4:25am, Rupert wrote:
I came up with many solutions that work in some cases  . I meant that a
general solution would have to include finding out what yes/no means. |
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Actually, Jon meant that he believes that in any ONE solution that works for all cases, there will be SOME "cases" (defined by sequences of answers) in which you cannot resolve the words for "yes" and "no", whereas with certain other "cases" you will be able to deduce the meanings.
on Aug 15th, 2002, 4:25am, Rupert wrote:
BTW, I dreamt of this! I was in a cafeteria with two waiters, one of them needed to be lied to, the other needed the truth... |
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Cool!!!  But where's GibberKnexus??
Best,
Eric
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Eric Yeh
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Re: Brainstorm
« Reply #53 on: Aug 15th, 2002, 5:29am » |
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Oops, didn't see this new page!
on Aug 15th, 2002, 4:48am, Rupert wrote:
Good one. I didn't notice that. Well, not good, really.
What if I asked a question like "If you are Knexus then Qa, otherwise Qb"? Would Knexus answer Qa or Qb? Eric?
(I'm afraid I won't like the answer... )
Cheers |
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Sorry: yes-no questions only, as per the standard rules.
on Aug 15th, 2002, 4:55am, Rupert wrote:
Thanks Eric,
Hm. Do you mean there are certain paths where we don't need to find out (this is what I understand Jon meant), or is it generally not necessary? (Don't answer if it gives away too much)
(I'm in Germany)
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Yes, paths.
Best,
Eric
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Rupert
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Re: Brainstorm
« Reply #54 on: Aug 15th, 2002, 5:48am » |
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on Aug 15th, 2002, 5:29am, Eric Yeh wrote:
Sorry: yes-no questions only, as per the standard rules.
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Qa Qb were supposed to be some question. As in "If you're Knexus, is A Knight, otherwise is 5=7?"
But Knexus really would have to answer to 5=7 as I understand it. So it doesn't help anyway...
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Eric Yeh
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Re: NEW PROBLEM: The Gods of Gibberland
« Reply #55 on: Aug 15th, 2002, 5:50am » |
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Correct. Sorry I misunderstood your earlier message.
Best,
Eric
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Rupert
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Re: NEW PROBLEM: The Gods of Gibberland
« Reply #56 on: Aug 15th, 2002, 8:48am » |
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Maybe this is just some psychological experiment to find out how long you can convince someone to work on a problem to which there is obviously no solution just by claiming there is one?
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Eric Yeh
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Re: NEW PROBLEM: The Gods of Gibberland
« Reply #57 on: Aug 15th, 2002, 10:40am » |
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Oh oh, you've got me!!! I myself am working on a open-ended problem from another puzzle web site: "Model the average length of time spent by strangers on a newly created impossible problem as a function of the credibility of the author. Determine the amount of credibility which maximizes that length of time."
Unfortunately, I am not bright enough to solve this on my own, so I am forced to study the problem empirically. A couple of years back I tried using credibility = 0; now I am experimenting on using credibility = 1 solveable new problem. Failing this, I will try again in a couple of years by first issuing two solveable problems, and go from there.
Best,
Eric
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Rupert
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Re: NEW PROBLEM: The Gods of Gibberland
« Reply #58 on: Aug 15th, 2002, 11:35am » |
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Ha! I knew it.
Nice touch btw to get Tim to indicate that he found the solution.
Now where's my tinfoil hat?
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Eric Yeh
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Re: NEW PROBLEM: The Gods of Gibberland
« Reply #59 on: Aug 15th, 2002, 11:40am » |
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Ye, we are all in on it together! Jon is only pretending he's looking for a soln.
Sorry, what's this hat thing? Is this some German reference I'm missing?
Evilly yours,
Eric
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| « Last Edit: Aug 15th, 2002, 11:41am by Eric Yeh » |
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Rupert
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Re: NEW PROBLEM: The Gods of Gibberland
« Reply #60 on: Aug 15th, 2002, 12:12pm » |
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on Aug 15th, 2002, 11:40am, Eric Yeh wrote:
Sorry, what's this hat thing? Is this some German reference I'm missing? |
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Tinfoil hats keep aliens/black helicopters from reading your mind and/or remote controlling your brain.
You mean you don't have one?
But then again, you are probably sitting IN the black helicopter.
And I shouldn't have told you...
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Eric Yeh
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Re: NEW PROBLEM: The Gods of Gibberland
« Reply #61 on: Aug 15th, 2002, 12:14pm » |
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Say, is that Illuminati???!!
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| « Last Edit: Aug 15th, 2002, 12:14pm by Eric Yeh » |
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Jonathan_the_Red
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Re: NEW PROBLEM: The Gods of Gibberland
« Reply #62 on: Aug 15th, 2002, 1:05pm » |
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Don't have much time (that stupid 'real life thing')... just wanted to pop in and acknowledge my error earlier re. the simpler problem where the Gods all tell the truth. Sigh...
Here are three questions that really do work in that case.
(hidden color to prevent spoilage)
Ask God A:
Q1: Is the word that means "yes" alphabetically before the word that means "no" if and only if you are GibberKnight?
God A answers: "foon".
Ask God A:
Q2: Does "foon" mean "yes" if and only if you are GibberKnave?
Case 1: God A answers "foon". In this case, he is GibberKnave
Case 2: God A answers "blatz". In this case, he is GibberKnexus
Case 3: God A answers "worple". In this case, he is GibberKnight.
For Q3, just use the iff trick to ask about one of the two gods you don't know.
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| « Last Edit: Aug 15th, 2002, 1:12pm by Jonathan_the_Red » |
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Eric Yeh
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Re: NEW PROBLEM: The Gods of Gibberland
« Reply #63 on: Aug 15th, 2002, 1:09pm » |
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Without checking the details, yes, something like that would work. Good job Jon!
Perhaps you want to put it in [colors] so prevent spoilage? 
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| « Last Edit: Aug 15th, 2002, 1:10pm by Eric Yeh » |
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Jonathan_the_Red
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Re: NEW PROBLEM: The Gods of Gibberland
« Reply #64 on: Aug 15th, 2002, 1:15pm » |
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Good idea. Just so I'm clear, the above solution works only if all three Gods tell the truth... but I'm pretty sure that it can be modded to work for the "real" case. I'll poke away at it this weekend.
BTW, this is not at all a big deal, but I prefer Jonathan to Jon. Just FYI.
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Eric Yeh
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Re: NEW PROBLEM: The Gods of Gibberland
« Reply #65 on: Aug 15th, 2002, 1:19pm » |
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Ye ye, I knew that. If it were the real deal I would've checked it a little more carefully!! Ye, the expansion requires a "second innovation" to get the knexus personality to fall in line, but you're certainly on the right track.
But Jonathan is too long to type!!! What will happen if I keep calling you Jon? You said you were difficult to offend, after all!!!!!
Best,
Eric
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| « Last Edit: Aug 15th, 2002, 1:19pm by Eric Yeh » |
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Rupert
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Re: NEW PROBLEM: The Gods of Gibberland
« Reply #66 on: Aug 15th, 2002, 1:58pm » |
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Hm. Relying on alphabetical order would be less than elegant.
Not only because of ambiguos sounds like e.g. s/c or h/j in some languages. What about that African toungue-popping consonant, or what if 'no' sounds like shattering glass and 'yes' sounds like a trumpet? These guys are some weirdo GibberGods after all, and "the language spoken in Gibberland is so unintelligible [...]".
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Eric Yeh
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Re: NEW PROBLEM: The Gods of Gibberland
« Reply #67 on: Aug 15th, 2002, 2:01pm » |
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This is true; "better" (i.e. more universal) conditions that accomplish similar things can be found.
Rupi, didn't I tell you not to read that msg??!
Best,
Eric
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Rupert
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Re: NEW PROBLEM: The Gods of Gibberland
« Reply #68 on: Aug 16th, 2002, 3:19pm » |
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Hi Eric,
I didn't get your mail until after I read the comment. But I actually found it to be more of a distraction than a hint. So no harm done.
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Eric Yeh
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Re: NEW PROBLEM: The Gods of Gibberland
« Reply #69 on: Aug 16th, 2002, 4:05pm » |
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Fair enough. Sorry I haven't gotten a chance to look carefully at your msg yet (tho things fine); been a bit busy at work.
Best,
Eric
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Jonathan_the_Red
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Re: NEW PROBLEM: The Gods of Gibberland
« Reply #70 on: Aug 16th, 2002, 6:43pm » |
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As Aristotle said when he entered his bath, "Fabreka!" (literally, "I have found the fabric softener!")
I'm not terribly thrilled with this solution (I find it a bit clunky), but it does work (*). Hidden with color tags... 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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That was quite a doozy. More commentary below hidden by color...
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The key to this one, of course, is to come up with a question that will force a Knight to give one of the answer words and a Knave to give the other, regardless of which word means 'yes' and which means 'no'. I used alphabetical order for the purpose... if there's a cleaner way, I'd like to know it.
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Thanks, Eric, for the hours of mental exercise
(*) At least, I think it works. If not, wouldn't be the first time I've been mistaken when I thought I had a solution...
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| « Last Edit: Aug 16th, 2002, 6:45pm by Jonathan_the_Red » |
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Eric Yeh
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Re: NEW PROBLEM: The Gods of Gibberland
« Reply #71 on: Aug 16th, 2002, 6:59pm » |
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Nice job Jon!! Ye, that is pretty much it! I'm not sure why you call it 'clunky'; I think it's pretty good! The first two questions make it truly elegant!!!
Something hidden:
Yes, the alphabet part is potentially problematic because they don't have to use an English alphabet, and even if they do there's no guarantee that you will be able to recognize their pronunciation. But you certainly have the right spirit. I think the most universal proposition to use is "The word I would find more aesthetically pleasing immediately after hearing the second word..." This taps the omniscience of the gods, but hey, omniscient is omniscient!!! And there's no arguing that it will have an answer which the questioner will know. Satisfactory, I hope?
OK then, I will wait a little bit more for last answers to trickle in, and then maybe post a breather or so before moving on!!!
Best,
Eric
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| « Last Edit: Aug 16th, 2002, 7:01pm by Eric Yeh » |
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Rupert
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Re: NEW PROBLEM: The Gods of Gibberland
« Reply #72 on: Aug 16th, 2002, 8:12pm » |
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Jonathan,
I'm surprised that it is possible after all with such simple questions. (The solution I came up with has questions about 8 lines long when written out in plain English.) -- I'll let you see in a private message.
Good job.
Rupert
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Rupert
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Proposed Extension to Riddle
« Reply #73 on: Aug 17th, 2002, 9:28pm » |
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How about an extension to the riddle?
You may not speak to the Gibbergods directly, but rather you have to relay your questions through a herald. You must tell him all three questions at once. Unfortunately, he is rather confused. He is neither able to select from several questions depending on previous answers, nor does he remember which of the gods he was supposed to ask which question. I.e. all he can do is repeat the three questions in the right order, randomly addressing one of the gods for each question.
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Eric Yeh
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Re: NEW PROBLEM: The Gods of Gibberland
« Reply #74 on: Aug 17th, 2002, 10:13pm » |
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Rupi,
It's a good initial thought, but in the end not a good idea. 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. That is why I have only been challenging people to do it that way after they give me a first soln.
Best,
Eric
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