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[GreatJustice]

Leafsnail basically solved it, though I suspect he wasn't the first. This IS a pretty old puzzle, after all.

The initial problem (the goats and doors problem) is only really tricky if you consider whether the game show person actually chose a random door, or chose one of the two doors with goats. If he doesn't know which door holds the car, then he has a 1/3 chance of opening the door with the car on the first go, meaning if you hold you STILL have a 1/2 chance of getting the car after he finds the goat. If he does know which door holds the car, and always picks the option without the car, then your chances of being correct without switching are still 1/3 and thus changing is probably better.

It isn't exactly "fair", though, since the odds are dependent on the rules of the game show ("Can the announcer actually randomly pick the car on the first run?") rather than actual probability.

[GlyphGryph]

(I don't think we've been working on that question for several pages. )

[GreatJustice]

Well, that's what I mean by "Leafsnail solved it". See:

Question 1: "What would someone with the opposite truth/lies configuration to you say that the random god's response will be this time?"
Odd guy out is the random god, set him to one side.

Question 2 (directed at either non-random god): "What was your response to the previous question?"

This identifies all three, but it's occurred to me that these aren't exactly yes/no questions, even if in both cases their answers are obviously going to be yes/no.  I'll try and rework them to be true yes/no affairs.

"If you tell the truth the answer is no, if you lie the answer is yes, of you are random and are telling the truth the answer is yes, if you are random and are telling the truth the answer is no. Who are you?"

That's not a question, it's a set of instructions.

[Neonivek]

Well, that's what I mean by "Leafsnail solved it".

He didn't.

Odd guy out is the random god, set him to one side

The random god may answer the same way. Creating a three yes or three no situation.

Plus... his question is invalid anyway. Since it isn't "yes or no". It is "Truthfully or false"

[Darvi]

Well the second question can be substituted with "Did you answer the last question with *insert word that was given as answer*?"

But yeah, that's kinda what I had figured out at the very beginning, but discarded it for only having 50% chance of success.

[Neonivek]

Well the second question can be substituted with "Did you answer the last question with *insert word that was given as answer*?"

That would be the way to tell the truth from lie.

"Is the Sky Blue"

ABB

"Did you answer *Blaw*" to A

Establish he tells the truth or lies.

Since the person who tells the truth will say the same thing twice. The Liar will say the same thing twice (No sky isn't blue, no I didn't say no again).

Nope

I need a way to get truth to say yes twice. And no to say two different answers. But I forgot how it is phrased.

[GlyphGryph]

We never figured out a way to determine the random person with question one, is the problem.

However, asking about the previous question IS a good second question.

Okay, first question: Is this dude random? (to everyone)

Odd man out is non-random - either liar or truthteller. Ask him the truth value of his answer to the previous question. Now you know whether he's the liar or the truthteller... Although you still don't know whether the answer is true or false.

However, you can now ask him "Is blah false?", knowing whether he'll answer truthfully or not, and then use THAT to determine (retroactively through the first question) the random guy, and then you're done.

Err... wait, I think messed up there.

[Neonivek]

I am just convinced the first question cannot be anything but the ABB

But there is a question you can ask to establish if one person lies or tells the truth with the second individual question.

I just forgot how it goes.

[Jelle]

You switch door ofcourse.

If one of the goats is revealed before you make a first pick it is indeed fifty fifty chance, if you pick a door and then then one of the goats gets revealed the leftover unpicked door has a 2/3 chance.
I might have messed up my logic here but the act of revealing one of the goats after a pick has been made gives significantly more information then simply revealing one of the three doors initially, since the picked door is never revealed I think it was?
Makes it 1/3 for picked door and 2/3 for either of two unpicked, after revealing it's 2/3 for the remaining unpicked door since the revealing tells you nothing about the door you picked.

I'm bad at explaining my train of thought and it's late so don't shoot me down.

Edit: Dang, this topic got large fast I hope this was still relevant.

[Frumple]

Huh. How are you folks telling which answer is a yes and which one is a no? I think I missed th'trick to figuring that out.

[Neonivek]

Huh. How are you folks telling which answer is a yes and which one is a no? I think I missed th'trick to figuring that out.

Quite a few of them are not and think they know the answer. Reelya is a good example.

[Reelya]

3 Gods questions.

(Q1) to all 3: anything that separates 1 guy from the other 2, such that the 1 guy is Truth or Liar. Easy.

2nd question to the man on his own:

(Q2) "If i asked you "are you the liar" would your answer be 'A'? "

Call the possible responses A and B

If this guy is the truth teller:
- if A=true: he'd answer "no"("B") to "are you the liar", therefore "no" (B) to Q2
- if B=true: he'd answer "no"("A") to "are you the liar", therefore "yes" (B) to Q2

If this guy is the lie teller:
- if A=true: he'd answer "no"("B") to "are you the liar", therefore "yes" (A) to Q2
- if B=true: he'd answer "no"("A") to "are you the liar", therefore "no" (A) to Q2

So the liar will always answer with 'A' to this question, and the truth teller with 'B'

We now know whether the questioned person is truthful or lies, but no whether A or B indicate truth. We can use the same trick on the third question. Point at one of the other Gods and ask:

(Q3)  "If i asked you "is that the random God?" would your answer be 'A'? "

If this guy is the truth teller:

*pointing at Random God:
- if A=true: he'd answer "Yes"("A") to "is that the random God?", therefore "Yes" (A) to Q3
- if B=true: he'd answer "Yes"("B") to "is that the random God?", therefore "No" (A) to Q3

*pointing at False God:
- if A=true: he'd answer "no"("B") to "is that the random God?", therefore "no" (B) to Q3
- if B=true: he'd answer "no"("A") to "is that the random God?", therefore "yes" (B) to Q3

If this guy is the lie teller:

*pointing at Random God:
- if A=true: he'd answer "No"("B") to "is that the random God?", therefore "Yes" (A) to Q3
- if B=true: he'd answer "No"("A") to "is that the random God?", therefore "No" (A) to Q3

*pointing at Truth God:
- if A=true: he'd answer "Yes"("B") to "is that the random God?", therefore "no" (B) to Q3
- if B=true: he'd answer "Yes"("A") to "is that the random God?", therefore "yes" (B) to Q3

So, after Q2 we know whether the isolated god from Q1 is true / false, and from Q3 we know which of the other ones is Random.

[Darvi]

-snip-

That hasn't been relevant for over two hours, are you a time traveler?

[Pnx]

(Q1) to all 3: anything that separates 1 guy from the other 2, such that the 1 guy is Truth or Liar. Easy.

(Q2) "If i asked you "are you the liar" would your answer be 'A'? "

(Q3)  "If i asked you "is that the random God?" would your answer be 'A'? "

I suppose this works, but you could have just asked them, "Is the sky blue", "Are you a liar", and "Is contestant #2 (or whatever) the random one?"

[Neonivek]

Yep because "Yes No" and "No, No"

Anyhow... another logic puzzle hmm...