Myth: A New Age CYOA

[Nevill]

If I may, let's make it so that a question needs 3 votes to be asked. Otherwise it is going to be... messy.

Also, can a question be addressed to all of them, and does it count as a single question, or as 3?

Edit: or a suit of votes, yes.

 

[Fangshi]

If I may, let's make it so that a question needs 3 votes to be asked. Otherwise it is going to be... messy.

Sounds good. I am in a good mood today so I won't willfully try and sabotage your efforts. 3 votes minimum for a question to ask it.

Also, can a question be addressed to all of them, and does it count as a single question, or as 3?

Each question can only be asked to a single golem. So if you ask them all the same thing it will count as three separate questions.



Also, I will try to keep a close eye on the thread but if I do not respond quickly it is because I am relaxing and playing S.T.A.L.K.E.R in the other window.

 

[Kz3r0]

Did you want answers to those now or some time to discuss? To clarify, phrasing a question with Derryth: "question" is a request for an answer from me. So that would burn through two questions right away.

Time to discuss, thank you.

I really want to do it in just two questions, a brainstorm is in order.

 

[Grimgravy]

Seems like "the hardest logic puzzle ever"

 

[Kz3r0]

I think that I have already logically determined that is either Golem A or Golem C, without the need for any question.
Someone sees a fault in my reasoning?

 

[Nevill]

I think that I have already logically determined that is either Golem A or Golem C, without the need for any question.
Someone sees a fault in my reasoning?

The information from one of the golems is 'noise'. You can't base anything on that golem's answer:

Golem A, Does Golem C always says the truth?"
Golem B, Does Golem A always says the truth?"

A yes and a no: could be tthat B is the Golem that sometimes lies and sometimes tells the truth, so we are certain that A lied.

Or that B is a liar, and A is random. That would still determine C as true.

A no and a yes: means that B is the Golem that sometimes lies and sometimes tells the truth, so we are certain that A tells the truth.

Or that C tells the truth, B is a liar, and A is random.

 

[Kz3r0]

I think that I have already logically determined that is either Golem A or Golem C, without the need for any question.
Someone sees a fault in my reasoning?

The information from one of the golems is 'noise'. You can't base anything on that golem's answer:

Golem A, Does Golem C always says the truth?"
Golem B, Does Golem A always says the truth?"

A yes and a no: could be tthat B is the Golem that sometimes lies and sometimes tells the truth, so we are certain that A lied.

Or that B is a liar, and A is random. That would still determine C as true.

A no and a yes: means that B is the Golem that sometimes lies and sometimes tells the truth, so we are certain that A tells the truth.

Or that C tells the truth, B is a liar, and A is random.

C it is then?

 

[treave]

Did you want answers to those now or some time to discuss? To clarify, phrasing a question with Derryth: "question" is a request for an answer from me. So that would burn through two questions right away.

If everyone would prefer I can run it like a minor vote where you put together a suite of two or three questions and vote for them. Once an option has sufficient support I could then answer it if that would work better?

Or I can just do this as a first come, first serve sort of thing. It would be easier for me but you are all spread out through different timezones and I would rather everyone has a say.

I think you could also split up the questions if you wanted: perhaps vote only on what the first question should be, and to which golem, before moving on to voting for the following question. And then finishing with either a vote for the correct answer, or voting for more questions. Step by step.

Though that might take too much time.

 

[Nevill]

C it is then?

No. Or/or.

A 'no' and a 'yes' means that it is either C or A, and you don't know which one even if you knew what passes for 'yes' and 'no'.

 

[Fangshi]

Though that might take too much time.

Well I am in no rush so if the voters want to go step by step we can certainly do that.



Opinions, voters?

 

[Nevill]

What use is one step if you don't have a follow-up ready?

I believe it can only be meaningfully solved as a whole.

 

[Kz3r0]

I think that I have already logically determined that is either Golem A or Golem C, without the need for any question.
Someone sees a fault in my reasoning?

The information from one of the golems is 'noise'. You can't base anything on that golem's answer:

Golem A, Does Golem C always says the truth?"
Golem B, Does Golem A always says the truth?"

A yes and a no: could be tthat B is the Golem that sometimes lies and sometimes tells the truth, so we are certain that A lied.

Or that B is a liar, and A is random. That would still determine C as true.

I reread this, how B can be a liar?
The question is if A always says the truth, if B says no is either true and in this case is not a lie and if false is impossiible for the same reasons that two yes are impossible.

A no and a yes: means that B is the Golem that sometimes lies and sometimes tells the truth, so we are certain that A tells the truth.

Or that C tells the truth, B is a liar, and A is random.

In short my reasoning was correct, is either A or C, we should devise some question for these two to determine which is the one that always tells the truth.

 

[Nevill]

I reread this, how B can be a liar?
The question is if A always says the truth, if B says no is either true and in this case is not a lie and if false is impossiible for the same reasons that two yes are impossible.

Sorry, my bad. Still, I don't see how you can ask a question to discern between the two if there is a possibility that one of them can tell things at random.

I'd say this might require another approach. We must accept that at least one of the questions could be almost completely meaningless if asked to the random golem. No information could be discerned from its answer. So we might take a closer look at a more trivial problem, where we 'know' the question was wasted, and there are only two golems left who speak either truth or lies. In that case, the question would be:

- If I asked the other golem if you speak the truth, would he reply in high tone?

If the golem replies in low tone, he would be the one speaking the truth.

Now we need to work our way up and add more conditionals to the question so that it would encompass the existence of the third "random" golem.

 

[Smashing Axe]

I've gone over this before as part of a logic course. So I should probably stay out.

I will say though that the first thing you want to do is to eliminate one of the three as not being random.

 

[Nevill]

Ok, so doing it in 4 turns is easy. The question that needs to be asked to each golem is this:

- If I asked the other golems if you speak the truth, would they always reply in high tone no matter how many times I ask (e.g. if and only if they aren't speaking randomly)?

A liar would answer this in high tone - if it means 'yes', then 'would always reply yes' part would be wrong, so the liar would answer that it is correct; and if it means 'no', then he would protest. Either way, the tone stays the same.

Similarly, a truth-teller would always answer in low tone. The random golem would answer at random.

Now, we would have either this 1) A: high tone; B: high tone; C: low tone, or this 2) A: high tone; B: low tone; C: low tone. If 1, then C is the one telling the truth. If 2, then A is a guaranteed liar, and we can ask him a simple question about, say, C - "Is C always telling the truth?". If he says no, then C is our guy, if he says yes, then it's B.

There must be a way to unite some of these questions in a single construct.

I will say though that the first thing you want to do is to eliminate one of the three as not being random.

Sure. How do you do it in 1 question, though?

Do you know the solution?

Edit: and I missed the fact that we still don't know the meaning of high and low tones. So my solution is actually 5 turns long. Ideas how to optimize it would be welcome.

 

[Smashing Axe]

Just ask a question that true and false cannot answer but random can.

 

[Kz3r0]

Just for curiosity' sake:
1-A Bronze Golem
2-B Silver Golem
3-C Golen Golem

 

[Nevill]

Smashing Axe, are you sure your solution works?

I am trying to come up with one that utilises something akin to the liar paradox, but the problem with questions that are neither true nor false is that the random golem can't answer them, too. It may lie or tell the truth, but it still operates under the same rules.

And we need to address it to the right creature, too. What if you address it to the one that is not random? You'll learn that it isn't... and that would be it.

 

[Zero Credibility]

Two noes: Means that none of them says always the truth.

Ok, maybe it's just my lack of sleep, but I admit I don't see this. How can you eliminate any of them if they both say no? Maybe A is always telling the truth (and C is a lying bastard while B is random), maybe B is (and A is random), maybe C is (while B is random). Or am I misunderstanding the problem or what you are saying here?

 

[treave]

Smashing Axe, are you sure your solution works?

It does. Without giving too much away, the hint lies in random being random, as stated in the update.

 

[Kz3r0]

Two noes: Means that none of them says always the truth.

Ok, maybe it's just my lack of sleep, but I admit I don't see this. How can you eliminate any of them if they both say no? Maybe A is always telling the truth (and C is a lying bastard while B is random), maybe B is (and A is random), maybe C is (while B is random). Or am I misunderstanding the problem or what you are saying here?

I am not very lucid too.
In the case of two noes B can be the one that always says the truth too.
So we are back to square one.

 

[Azira]

I've googled the riddle, so I probably should also keep my mouth shut.

 

[Nevill]

So basically, if we guess the magic question for the random golem, it is easy to do it in 3 turns.

Solution 1:
1. Ask golem A the magic question
1a. If A is random, proceed with the trivial solution.
2. If A is not random, ask golem B the same question. This invariably determines the random golem.
3. Proceed as in 1a.

Solution 2:
1. Ask golem A the question as in the 5-turn solution.
2. Ask golem B the same question.
3a. If (A=lt, B=lt, C=?), ask B the magic question, pick the non-random golem.
3b. If (A=ht, B=lt, C=?), ask C the magic question, pick the non-random lt-option.

I am sorry, I am clueless as to how to determine the random guy in just 1 question. I haven't even got a clue to what the question is in the first place.

Fangshi, how resistant are those golems to division by zero? Because all I have is taking two sequences of 1 and -1 corresponding to yes or no answers, having two of the guys sum their results over an infinite amount of answers to the same hypothetical question and having the third guy divide by the limit of the resulting sum. And then comparing the result to zero to turn it into a simple yes or no question.

Yes, I lack imagination that much.

 

[Zero Credibility]

So, everyone that knows the answer here is keeping quiet. I hope you guys will at least say something if the rest of us get it wrong. You are participating and not just spectating here, right?

Anyway, going on the hint that we need to find one that isn't random, how about this question:

Golem X, if I asked the other two if you always tell the truth, would their answers be the same or not?

If X is not the random golem, he can't answer that one because he doesn’t know the answer himself (because he doesn't know how the random golem will answer) and can't tell the truth or lie. If he is random he can because he would know the answer (and wouldn't care about it anyway).

 

[Smashing Axe]

Don't have "or not" with that first question, if you want to be really pedantic the correct answer will be yes regardless of what the other golems would answer. You also need to work out how to phrase the later question/s in a manner that incorporates our ignorance of what yes and no mean.