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Eric Yeh
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 NEW PROBLEM:  The Gods of Gibberland   « on: Aug 8th, 2002, 2:09pm » Quote Modify

Hello everybody!  After a four-year hiatus since "Past, Present, Future", this great new forum--so packed with people I have so quickly developed a great respect for--has inspired me to create a new series of puzzles!  Here is one that I really like.

Caveat:  This problem may sound impossible -- I should know, I spent many hours thinking about it and several variants, and at one point summarily rejected this proposal as having no possible solution!  "What a cool one it would be," I thought, "if only it were actually solveable!!!"

What a great surprise it was, then, when I later had a revelation that seemed to provide a workable solution!!!!!  However, I must admit that this problem, unlike PPF, comes to you guys with an insufficient amount of "playtesting".  I've held back on posting it to try to get at least one independent confirmation of my solution, but none of my friends has yet been able to solve it!  (In their defense, I only gave them a day or so to try it, and of course we all have work or something else to do...).

So there is always a possibility that there is some flaw in my solution, although I consider it highly unlikely.  Even so, perhaps there would be another solution I hadn't thought of?  So if you guys find it as interesting as I did, perhaps you can delve into it with me...

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THE GODS OF GIBBERLAND THE GODS OF GIBBERLAND THE GODS OF GIBBERLAND THE GODS OF GIBBERLAND THE GODS OF GIBBERLAND THE GODS OF GIBBERLAND THE GODS OF GIBBERLAND THE GODS OF GIBBERLAND THE GODS OF GIBBERLAND THE GODS OF GIBBERLAND THE GODS OF GIBBERLAND THE GODS OF GIBBERLAND THE GODS OF GIBBERLAND THE GODS OF GIBBERLAND

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 three questions, determine which god is which.

[Notes:

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.

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

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Yes, this problem is designed to be anti-programming, anti-da/ya-algorithm, and besides that, beyond the traditional da-ya problem.  I have written up some hints on it, but I don't want to hand them out quite yet...  Who knows, maybe you'll all find it to be trivial!

In any case, please let me know if anything is unclear!!!!!

Happy Puzzling,
Eric
 « Last Edit: Aug 8th, 2002, 2:11pm by Eric Yeh » IP Logged

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Drake
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 Re: NEW PROBLEM:  The Gods of Gibberland   « Reply #1 on: Aug 8th, 2002, 4:01pm » Quote Modify

It's unclear to me as to whether the Gods themselves behave like their worshippers.. In other words if you ask GibberKnave how a Knave would answer, would he lie about what the Knave would say (thus negating the Knave's answer)?

Or do the Gods always give a truthful answer?

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Eric Yeh
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 Re: NEW PROBLEM:  The Gods of Gibberland   « Reply #2 on: Aug 8th, 2002, 4:04pm » Quote Modify

Sorry for the confusion; I guess I should have clarified:  the gods behave as do their constituents.

Best,
Eric
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bartleby
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 Re: NEW PROBLEM:  The Gods of Gibberland   « Reply #3 on: Aug 9th, 2002, 8:28am » Quote Modify Remove

Knights always answer the truth, knaves always lie, and knexuses always answer the xor of what the knight and knave would answer.

OK, let me ask the obvious question:  So if I ask them all the same question that has an answer of Yes, GibberKnexus will always answer something that means "Yes", then?  Because if GibberKnight always answers Yes to my always-Yes question, and GibberKnave always answers No, then GibberKnexus will have to answer "Yes", right?
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Eric Yeh
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 Re: NEW PROBLEM:  The Gods of Gibberland   « Reply #4 on: Aug 9th, 2002, 8:33am » Quote Modify

Often the case, yes!  But not always.  Observe:  Are you a knight?

Best,
Eric
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Eric Yeh
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 Re: NEW PROBLEM:  The Gods of Gibberland   « Reply #5 on: Aug 9th, 2002, 9:03am » Quote Modify

Sorry -- just re-read your msg and realized I missed the part about asking a "yes" question.  So the answer is that yes, a knexus would always respond "yes" to such a question.

Best,
Eric
 « Last Edit: Aug 9th, 2002, 10:41am by Eric Yeh » IP Logged

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Drake
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 Re: NEW PROBLEM:  The Gods of Gibberland   « Reply #6 on: Aug 9th, 2002, 11:33am » Quote Modify

Darn you!  I have not been able to stop trying to figure this one out since I read it last night.. It kept me up for a couple hours thinking about it.    But I keep going in circles.  I can solve it if I could ask 4 questions, but can't seem to do it in 3.  If it were not for the language barrier this would be easy enough, but due to that you need to really figure out 4 pieces of information (the language, and the identities) with 3 questions.

I'm going to put down my reasoning thus far.  Let me know if I'm on the right track or if I've taken a detour..

First, I'll refer to the 3 Gods as A, B, and C.  I drew up a truth table based on their answers.

I started out thinking that the first thing to do is get a baseline for the language by asking A a question that he must respond No to.  So I ask A, "Are you the God of the Knaves?" to which he must say No, and therefore I know the word for "No".

I then ask A a second question, "Are you the God of Knights?".

If he answers "No", then he must be GibberKnexus, as both the others would have said "Yes".  It's then easy to figure the other 2 out by asking B, "Do knights ever lie?".  If the answer to this is "Yes", the B is GibberKnave, and C is GibberKnight.

If A Answered "Yes" to the second question however, Then I'm stuck.  This means A is either GKnave or GNexus, and either B or C is GKnight.  I can then either figure out which is GKnight OR whether A is GKnave or GNexus with one more question, but I'm still left without knowing who the remaining 2 are.

I've also tried this without a baseline to get the language down.
I can ask A and B each "Do knights ever lie", then if the answer sounds the same, then the sound means "Yes", and C is GKnight.  Then I ask A "Are you the god of Knights", to which he'll answer "Yes" only if he's GKnave.

But if the answer to the first 2 questioned sounded different, then I only know that A or B is GKnight, and that C is either GKnave or GKnexus.  I could ask the same question to C and figure out which is the Knight and what "Yes" sounds like at the same time, but then I'm left without knowing who the remaining 2 are once again.

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Jonathan_the_Red
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 Re: NEW PROBLEM:  The Gods of Gibberland   « Reply #7 on: Aug 9th, 2002, 11:38am » Quote Modify

on Aug 9th, 2002, 11:33am, Drake wrote:
 Darn you!  I have not been able to stop trying to figure this one out since I read it last night..

It's a doozy, all right. My computer program has made no headway

Quote:
 I started out thinking that the first thing to do is get a baseline for the language by asking A a question that he must respond No to.  So I ask A, "Are you the God of the Knaves?" to which he must say No, and therefore I know the word for "No".

This can't work. There are six possibilities for the arrangement of the Gods. If you spend a question getting the word for "No", you have to distinguish among those six possibilities with only four possible answer sets for the remaining two questions.
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Eric Yeh
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 Re: NEW PROBLEM:  The Gods of Gibberland   « Reply #8 on: Aug 9th, 2002, 11:41am » Quote Modify

Sir Drake:

First, many thanks for your enthusiasm on my puzzle!!!  I very much appreciate it!!!!!    Did you also solve my last one?

Now, if you really want my help, here's a clue to the first mistake in your reasoning:

You cannot waste an entire question to determine tha language; it will not leave you with enough discriminating power.

Good luck!!!
Eric
 « Last Edit: Aug 9th, 2002, 11:42am by Eric Yeh » IP Logged

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Eric Yeh
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 Re: NEW PROBLEM:  The Gods of Gibberland   « Reply #9 on: Aug 9th, 2002, 11:52am » Quote Modify

Woops, I guess Jon got to that one before me!  But I'm glad to know that I answered the right thing -- phshew!

Glad to hear you are thinking about it, too, Jon; this one was for you!    I was worried for a sec from your silence that I had offended you with my jokes!

BTW, how do you guys get the font color to precisely match the background?  Even when I am "smart" enough to look and see which background my post will get, I haven't been able to find the right color schemes!!!  I think I've seen you do it before perfectly, so that only a highlight illuminates the text?

Oh, and one last thing I meant to add to that last post to Drake:  The god GibberKnight asked that I relay that he prefers to be called by his proper name rather than his position (even though you only did it once).

Haha, ok so I'm in a weird mood just now.

Best,
Eric
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Jonathan_the_Red
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 Re: NEW PROBLEM:  The Gods of Gibberland   « Reply #10 on: Aug 9th, 2002, 12:33pm » Quote Modify

Eric--

Don't worry, I'm not easily offended

To match colors exactly, you need to know what color you're matching... the color scheme on this board alternates between #252525 and #444444. So:

The below text is hidden on a dark background
Hi there!

The below text is hidden on a light background:
Hi there!

The source for both of these:
Code:
 [color=252525]Hi there![/color] [color=444444]Hi there![/color]

 « Last Edit: Aug 9th, 2002, 12:36pm by Jonathan_the_Red » IP Logged

Jonathan_the_Red
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 Re: NEW PROBLEM:  The Gods of Gibberland   « Reply #11 on: Aug 9th, 2002, 12:34pm » Quote Modify

Repeating earlier color code so you can see it on the different background:
The below text is hidden on a dark background
Hi there!

The below text is hidden on a light background:
Hi there!
 « Last Edit: Aug 9th, 2002, 12:35pm by Jonathan_the_Red » IP Logged

Eric Yeh
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 Re: NEW PROBLEM:  The Gods of Gibberland   « Reply #12 on: Aug 9th, 2002, 12:48pm » Quote Modify

Excellent -- thanks dude.  How'd you get the color scheme originally?  O well, I'll remember it.

Ye, I guess I didn't really think you were offended, but I was disappointed that you weren't posting!!!

So, any progress on the problem?

Best,
Eric
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Jonathan_the_Red
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 Re: NEW PROBLEM:  The Gods of Gibberland   « Reply #13 on: Aug 9th, 2002, 12:56pm » Quote Modify

Eric--

Originally, I got the scheme by trial and error. Then I viewed the source of the web page and found it there.

Here's where I am so far on your problem...

The first question cannot give you any immediate information (with the apparently sole exception of "Are you a knave?") Because of this, you can't really have any dynamic strategies between your first and second questions... before asking anyone anything, you pretty much have to choose your first two questions and whether to ask them to the same God or a different God.

Your first question obviously cannot reference either of the two "answer words". Your second question, however, must reference the answer word you get from the first question. Proof left as an exercise for the reader

That's where I am so far. I'll keep chugging away.
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Joshua Franklin
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 Re: NEW PROBLEM:  The Gods of Gibberland   « Reply #14 on: Aug 9th, 2002, 1:06pm » Quote Modify Remove

(I really need to stop reading riddles before I go to work)

I just spent 2 hours coming up with questions and possible answers and almost came up with an answer, but then realized that it wouldn't work, and then came up with this chart and THEN the questions.

1.  Would you lie to me?
2.  Are you a God?
3.  Are you GibberKnight?
4. Are you GibberKnexus?

GibberKnight   GibberKnave GibberKnexus
1 No       No    No
2     Yes       No   Yes
3     Yes      Yes   No
4     No       Yes   Yes

I. Ask any god question 1 and 2.

Ia.  If it replies 'No', 'No', then it is GibberKnave.

IbAsk a different god question 3.  If it replies 'Yes', it is GibberKnight; if it replies 'No', it is GibberKnexus.

IIa.  If it replies 'No', 'Yes', it is GibberKnight or GibberKnexus.

IIb. Then ask a different god question 4.

This is where I believe there is a problem with the riddle (or my logic).  Because there are three people talking, if, after the first two questions, you don't know at least 1 of the gods, you are pretty much S.O.L.

I've followed my chart down every permutation, and if you start with either GibberKnight or GibberKnexus, and then move (or stay) to GibberKnight or GibberKnexus, because of the XOR, it becomes impossible (I think) to solve the problem.  There will always be two Gods who answer in the same way, keeping the ambiguity.

I've been looking at this for 3 hours now, so I'm going to take a break and clear my head.  I don't even know if I'm explaining myself well anymore--that's how muddled I am (try figuring out how GibberKnexus would answer: "Would GibberKnight answer 'Yes' to the question: 'What would GibberKnave tell me if I asked him if he was GibberKnexus'?")  Lol, I thought it might help.
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Eric Yeh
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 Re: NEW PROBLEM:  The Gods of Gibberland   « Reply #15 on: Aug 9th, 2002, 1:10pm » Quote Modify

Jon, you're right on as usual.  But now, riddle me this:  Why are you Red??!
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Jonathan_the_Red
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 Re: NEW PROBLEM:  The Gods of Gibberland   « Reply #16 on: Aug 9th, 2002, 1:11pm » Quote Modify

It's even worse, Joshua. The Gods don't answer "Yes" or "No", they answer in their own language, which you don't understand.

This puzzle really, really is tough.
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Joshua Franklin
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 Re: NEW PROBLEM:  The Gods of Gibberland   « Reply #17 on: Aug 9th, 2002, 1:12pm » Quote Modify Remove

Spent so long writing my post I didn't see everyone else's...oh well, guess I gotta go back to the drawing board....

btw--where can I send a bill to eric and william for all the asprin I've had to buy since finding this site?
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Joshua Franklin
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 Re: NEW PROBLEM:  The Gods of Gibberland   « Reply #18 on: Aug 9th, 2002, 1:15pm » Quote Modify Remove

Jon,

I know that.  That's why my first question established the word 'No'...Everyone answers 'No' to it, so I know what 'No' is, and if they say something different in the later questions I know it has to mean 'Yes'.
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Eric Yeh
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 Re: NEW PROBLEM:  The Gods of Gibberland   « Reply #19 on: Aug 9th, 2002, 1:28pm » Quote Modify

Josh,

Thanks for your enthusiasm!  Don't worry, you explain yourself well.  Here's my response:

I agree that you are "SOL" if you have not identified one god after your second question.  Hmmm.  Actually, that's not true.  But I will also be generous enough to say that my soln does identify one by two questions in.

As for your concluding puzzle (which I like as a subpuzzle!), the answer is:

Yes.

Best of luck!
Eric
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Eric Yeh
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 Re: NEW PROBLEM:  The Gods of Gibberland   « Reply #20 on: Aug 9th, 2002, 1:31pm » Quote Modify

on Aug 9th, 2002, 1:12pm, Joshua Franklin wrote:
 btw--where can I send a bill to eric and william for all the asprin I've had to buy since finding this site?

Send it straight to Will -- I'm only a limited liability partner.
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Drake
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 Re: NEW PROBLEM:  The Gods of Gibberland   « Reply #21 on: Aug 9th, 2002, 3:49pm » Quote Modify

No matter how I work it, I can only get it down to knowing one of the Gods for sure.. The other 2 are always ambiguous.

Any hints for us, Eric?  (BTW, that's my name too)
If I don't solve this today it's going to kill my weekend..

-- Eric
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Eric Yeh
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 Re: NEW PROBLEM:  The Gods of Gibberland   « Reply #22 on: Aug 9th, 2002, 3:55pm » Quote Modify

Hmm, well, I do feel bad for you Drake, I really do.  I think I am willing to help you out, but I don't want to give anyone else any clues.  Thus, I cannot use this forum.

Send me an e-mail (eyeh@post.harvard.edu) so I have your address and I will respond to you directly -- under the condition that you never post any clues or solutions to the forum.  (Only glowing words of praise -- haha jk.)

Best,
Eric
 « Last Edit: Aug 9th, 2002, 3:57pm by Eric Yeh » IP Logged

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tim
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 Re: NEW PROBLEM:  The Gods of Gibberland   « Reply #23 on: Aug 10th, 2002, 12:27am » Quote Modify

A small clue:
The price of knowing which god is which is that you can't always work out which word means what
That might just help someone.
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Eric Yeh
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 Re: NEW PROBLEM:  The Gods of Gibberland   « Reply #24 on: Aug 10th, 2002, 10:48am » Quote Modify

Tim,

Have you solved the problem?  You'll be the first person I know.

Best,
Eric
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