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/sci/ - Science & Math

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2632479 No.2632479 [Reply] [Original]

The Hardest Logic Puzzle Ever.

Pasta from Wiki:

The Hardest Logic Puzzle Ever is a title coined by American philosopher and logician George Boolos in an article published in The Harvard Review of Philosophy (an Italian translation was published earlier in the newspaper La Repubblica, under the title L'indovinello più difficile del mondo) for the following Raymond Smullyan inspired logic puzzle:
“ Three gods A, B, and C are called, in no particular order, True, False, and Random. True always speaks truly, False always speaks falsely, but whether Random speaks truly or falsely is a completely random matter. Your task is to determine the identities of A, B, and C by asking three yes-no questions; each question must be put to exactly one god. The gods understand English, but will answer all questions in their own language, in which the words for yes and no are 'da' and 'ja', in some order. You do not know which word means which. ”
Boolos provides the following clarifications:[1]
“
It could be that some god gets asked more than one question (and hence that some god is not asked any question at all).
What the second question is, and to which god it is put, may depend on the answer to the first question. (And of course similarly for the third question.)
Whether Random speaks truly or not should be thought of as depending on the flip of a coin hidden in his brain: if the coin comes down heads, he speaks truly; if tails, falsely.
Random will answer 'da' or 'ja' when asked any yes-no question.[1]

>> No.2632493

you ask a question to A or B and then do the opposite.

>> No.2632495

It's better if Random doesn't randomly answer truthfully/falsely but instead randomly says da/ja.

>> No.2632506

>>2632495
Its really the same thing.

>> No.2632509

>>2632493
One question each god.

Read rules.

>> No.2632518

No, it's not.

>> No.2632534

>>2632518
>>2632518
its the same thing for us.
Unless ur a tard then its a different thing.

>> No.2632568

$2

>> No.2632572

Is this even solvable?

>> No.2632581

>>2632572

Wikipedia says so.

brb reading.

>> No.2632601

>>2632509
>It could be that some god gets asked more than one question (and hence that some god is not asked any question at all).

Nope.

Also the answer to this riddle is simple: approach each god and ask them the same two questions:

1) If I asked you "is the sky blue," would you say "ja?"
2) Is the sky blue?

True will give the same answer for both. False will give different answers. Random is a faggot.

>> No.2632600

Ask God A: "What would B say?"
Ask God B: "What would A say?"
I'm not sure where to go from there..

>> No.2632609

I don't think it's possible to solve this.
You get 3 questions. This means you get a 3 levels-deep binary tree of options. As in, there are 8 possible results for your questions (yes,yes,yes; yes,yes,no; yes,no,yes etc.).
On the other hand, there are 6 possible ways to name the gods. This means that, in theory, every arrangements of the gods may have a series of answers that points to it.

The problem is with the ja and da. I don't see where in the system you have the information required to figure this out.

>> No.2632618

>>2632601
total of 3 questions only

>> No.2632632

>>2632601
You're only allowed 3 questions. You have six.

I just looked up the answer, and there's no fucking way I would have thought of it. And I don't think anyone on /sci/ would have thought of it either.

>> No.2632638

>>2632600
But that's not a yes/no question...

>> No.2632639

>>2632618
Sorry, I meant "any god."

I'm not sure how to handle Random. My method works if you utilize your 66% chance of not getting Random.

>> No.2632641

http://www.khanacademy.org/video/liar-truthteller-brain-teaser?playlist=Brain%20Teasers

>> No.2632650

1."Are you random?"
Ja
2."Are you random?"
Ja
3."Are you random?"
Da.

well fuck

>> No.2632654

wow this fucker is indeed hard.
Random answer? wow
We dont know what is yes or no?
fuck me i surrender

>> No.2632672

>>2632632
six? 3 or 6?
am confus

>> No.2632684

Ja fucks with my mind thanks to german

>> No.2632721

guise

random makes this impossible

>> No.2632730

>>2632721
if random makes it impo then 'ja' 'da' makes this beyond impossible.

>> No.2632744
File: 12 KB, 400x400, Wikipe-tan.png [View same] [iqdb] [saucenao] [google]
2632744

>>2632479
>Pasta from Wiki:

You mean "pasta from wikipedia", surely.

>> No.2632773

>>2632744
You like the full name?

>> No.2632786

>>2632632
Care to spill it?

>> No.2632787

If I asked him that Da and Ja are Yes and No in that order, would he tell me?
Ja
Is Da and Ja yes in that order? Da
Is Da And Ja yes in that order? Da
fu-

>> No.2632803

>>2632572

Yes. You ask a question that only Random can answer "Will you answer the same as Random?" to eliminate random. True and False are both unable to answer, whereas Random, of course, will spout nonsense and usual and will say something.

>> No.2632825

Anyone kind enough to explain?

>It could be that some god gets asked more than one question (and hence that some god is not asked any question at all).

Its one question per god, total of three gods, what is this?

>> No.2632834

>>2632803
Brilliant

Except false will bullshit you saying yes in his language

>> No.2632843

>>2632834

But he can't. He doesn't know whether what he'll say will be the same as Random or not, so he's forced into no answering.

>> No.2632850

>>2632825
No, no, you're allowed to only ask three questions. You may not ask the same god the same question twice in a row. But you can ask the same god two different questions. Not only was this clear with the rules as written, it was then clarified in the clarifications, and yet you still didn't understand it.

>> No.2632855

>>2632834

i don't think so, because that would only have a fifty fifty of actually being false, so he can't

he's just false, not evil, he operates on the same rules as true

>> No.2632859

>>2632850

Can you address a single question to all of them at the same time using up only one of your questions?

>> No.2632862

>>2632850
bullshit on your two in a row. that was never disallowed.

>> No.2632865

>>2632859
no, each question to only one god

>> No.2632869

can i ask them
"may i ask more questions?"
ask it till i hit the one that is lying
get the yes and make the game a lot more easy
>trollface.jpg

>> No.2632872

>>2632855

Yeah exactly. He'd only be able to answer if you said something like "Do you know if you'll say the same thing as Random to this question?" or whatever.

>> No.2632876

>>2632843
You are indeed brilliant.

1. Can you answer the same as Random and false?
says nothing (truth) says something (random) says something (false)
2. Will you answer the same as random?
(says nothing, he's false, says something, he's random)
3. isn't required

>> No.2632881

>>2632859
No, "each question must be put to exactly one god".

>> No.2632882

>>2632825
No one fucking said one question per god, it only says
>determine the identities of A, B, and C by asking three yes-no questions; each question must be put to exactly one god.
That means you can only address each question to one god. For instance you cannot say " God a and b, is Earth the 3rd planet from the sun?" It would be "God a, is Earth the 3rd planet from the sun?"

>> No.2632889

>>2632876
c'mon, somebody point out my flaw.
I really want to solve this

>> No.2632892

>>2632869
Only that by then the game would'v ended.
trollfist.jpg

>> No.2632896

>>2632876
mcfucking bump

>> No.2632901

>>2632889
The flaw is that the answers are in Yes Or No form.
No other answers.
Even if you wouldn't know what is yes or no.

>> No.2632902

>>2632876
c'mon /sci/, help me here

>> No.2632905

lets say B was random,

if you to ask A (whether A is T or F) what would B say, A cant answer the question, because he cant know what random would say

>> No.2632907

>>2632876

False can't answer the first question because he doesn't know if he'll say the same thing as himself AND random, but only the same thing as himself.

>> No.2632913

>>2632901

>>2632901
oh damn

>> No.2632916

>>2632905

They can only answer "da" or "na" as an affirmative or denial. They can't answer it as an objective answer.

>> No.2632926

can one of the questions be "does da mean yes?"

>> No.2632928

>>2632495
Tard

>> No.2632929

>>2632907

Disregard this. You put "Can" not "Will".

>> No.2632943

>>2632926
OP here.
ye you can.

>> No.2632982

i think this can not be solved god C fucks things up
too many variables when god C is around

>> No.2632987

everyone fails miserably.

Listen to this:
1.Is da yes?
2.Is ja no?
3.Is da no?
there you go.

>> No.2633005

>>2632987
you get three questions

each of the questions can only be answered by 1 god

>> No.2633026

>>2632987
lol you can't be sure which god is which after asking these questions
they may be ABC or CBA
may turn the exact same answers

>> No.2633029

>>2633005
tard?
where does it say that?
> Your task is to determine the identities of A, B, and C by asking three yes-no questions; each question must be put to exactly one god.

Its one question per god.

>> No.2633033

>>2633029
>It could be that some god gets asked more than one question (and hence that some god is not asked any question at all).
What you quoted means that you can't ask the entire group a question.

>> No.2633037

Read the answer to this a few years ago, and I know roughly what it was like, but even with that I can't figure it out anymore. Excellent puzzle.

>>2632889
You need to ask them a yes/no question. In this context it means that not only are the only potential answers yes and no, but the gods have to be able to answer with yes or no (i.e. they have to be able to evaluate the truth value of the answer).

>> No.2633040

>>2633029
nigga are you fucking stupid?

>It could be that some god gets asked more than one question (and hence that some god is not asked any question at all).

e.g. you can ask 2 questions to god A and 1 to god C

>> No.2633041

>>2632534
No, they're different, and if you ask nicely, I'll tell you why.

>> No.2633042

>>2633026
So?
This still solves the puzzle

>> No.2633050

>>2633029
double tard.

the question is to be put to exactly one god.

you cant ask them all a question. doesnt say you must ask them each a question.

wish i could change the font size to say how much of a TARD you are

>> No.2633052

>>2633041
ok, am being nice, sry.
Pls tell me why.

>> No.2633056

>>2633041
They're indeed different, but I'm not sure why you think it's better if the answer is random. In that case, the strategy of the anon above (ask an unanswerable yes/no question) can work.

>> No.2633057

>>2633050
Ok then, can you explain?
So you ask 3 questions to one god?

>> No.2633058

Ask each God this question, the one that can't answer is true

"Are you going to answer this question with the word that means no in your language?"

>> No.2633076

>>2633057

You can ask a total of 3 questions. You can only address one god at a time. You can address the same god more than once, but you cannot address multiple gods with one question. You can ask two gods the same question, but it would count as 2 of your 3 questions.

>> No.2633088

>>2633058
And as for the other two?

>> No.2633090

>>2633058
copying and pasting from wikipedia does not make you a genius

>> No.2633091

>>2633042
ok lets say you ask 1st question to god A
he answers No - da
2nd question to god B
he answers No - ja
3rd question to god C
he may say either Yes or No
for the example we would say he answers Yes

how does that imply which god is which?

>> No.2633098

>>2633088
You've just destroyed a God, fuck working out who's who

>> No.2633104

>>2633076
lol what a moron.
Its obvious that you have 3 questions.
And you ask ONE god each time.
And OBVIOUSLY you ask one god at a time.

When a riddle/puzzle/wth says you got 3 questions it means that you can ask 3 times total each one.
Whats red?
Whats red?
Whats blue?
Are three questions.
Even when i was 5 that was obvious to me.
Funny thing is that you need to point it out.
How stupid can you be for the love of these 3 gods.

>> No.2633107

>>2633058
doesn't differentiate between random and false

fail

>> No.2633129

so, "Will you give the same answer to this question as Random" identifies A as either Random or True/False.
If A's random, ask B "Are you True?", this determines the word for yes, since they will both answer yes. Then ask B "Are you a god?" This determines all three.
If's A's not Random, I don't fucking know.

>> No.2633140

>>2632479
The problem is Random always has the chance to completely imitate what True or False would say given the same question. So how could he ever be differentiated (with 100% chance) from either of them? Anyone?

>> No.2633149

>>2633076
Ty for your replay but:
>You can ask a total of 3 questions. You can only address one god at a time. You can address the same god more than once, but you cannot address multiple gods with one question. You can ask two gods the same question, but it would count as 2 of your 3 questions.

I can address the same god more than once?
So can i ask one god three questions?
And nothing to the other two.

>> No.2633158

>>2633149
Yes, that's correct. You can completely ignore B and C

>> No.2633172

how does each god answer this question:

will you give the same answer as true and false?

>> No.2633208

>>2632803

But what if the other gods can predict random due to being gods who can predict the outcome of coin flips?

>> No.2633247

>>2633208
no

>> No.2633253

None so far?
Most difficult question on /sci/ so far

captar:SCIENCE, titopeo

>> No.2633273

so finding true, with one question left, you can ask him who random is

>> No.2633401

God 1: Which god are you?
God 2: Which god are you?
God 3: Which god are you?

you should be able to figure it out based on their answers from there. The whole ja and da thing is to throw you off

>> No.2633408

>>2633401
Which god are you?
...
Which god are you?
...
Which god are you?
Da.

Well, shit.

>> No.2633419

>>2633408

Random can't answer ja or da to non-yes or no questions.

>> No.2633481

Lol I've seen this problem. I already know the solution, but I won't post it to see if you guys can figure it out. There's no way in hell I would have done it on my own, it took long enough to understand the solution once I stared at it long enough. It's ridiculously complex. But possible!

>> No.2633483

>>2633419
Actually none can answer other than yes-no

So "which god are you" is stupid.
As the answers can be in form of YES OR NO.

>> No.2633501

>>2633419
Random doesn't give a shit about the question, he ignores it and says Da or Ja

>> No.2633530

>>2633501
Random does care about the question as it's phrased. He determines whether "yes" or "no" is the true answer, and then randomly chooses to answer truly or falsely,

>> No.2633546

>>2633129
if A IS random ask the two following questions to god B:

>Does Ja mean yes?
True god will always answer Ja
False god will always answer Da
From this question you figure out if he god B is true god or false god

by process of elimination you also figure out who god C is as well

>> No.2633667

>>2633546
okay, so you figured out what I did in one less question. Doesn't solve the question of what to do if A isn't random.

>> No.2633675

>>2633667
Oh shit... wait!
If A isn't Random, ask A "Does Ja mean Yes" to determine A.
You now know A, and if you ask the first question to B, you figure out if he is Random or the other one, and you know god C through elimination!
/sci/, we've done it! Can anyone break our method?

>> No.2633676

>America
>stupid

there goes anther stereotype

>> No.2633756

>>2633129
I don't think that "will you give the same answer to this question as random?" is a valid yes/no question. the correct answer would be "I don't know" or "not enough information"

I saw this problem about a week ago. Here's my solution

Ask god A
"If I were to ask the alphabetically first god among B and C 'is B random?' would they answer ja?"
it turns out that an answer of da implies that C is definitely not random and an answer of ja implies that B is definitely not random.

then you ask the god that you know is not random "if I were to ask the other one of true and false 'is A random' would he say ja?"
da implies that A is random and ja implies that he is not

now that you have found out who random is you can distnguish between true and false by asking one of them "does ja mean yes?"

>> No.2633857

bump

>> No.2633895

1)What is 1+1?
2)
If only one gets it right then you know thats the true and you ask which of the two false are random, then you know A, B and C.
If two get it right (lets call them A and B) then you ask C which of the two is random. He will lie and you will then know A, B and C.

>> No.2633906

>>2633895
thats not a yes/no question

>> No.2633915

>>2633895
Sorry, thats an easy fix

Does 1+1=2

>> No.2633929

>>2633895
That requires 4 questions, plus you don't know what yes and no are.

>> No.2634047

>>2632479
It really isn't.
You ask one of them, "if I were to ask either of the other two gods what da or ja meant, would they both give the answer yes?".
Truth God and False God cannot answer, as they cannot know what Random God will say, and if you posed the question to Random God, he will give an answer.

Then one may ask - "Will the remaining god say ja is yes?" to each of the remaining gods. Then it can be determined like the classic liar-truthteller problem.

>> No.2634088

>>2634047
true and false won't know the answer which means your question is not a valid yes/no question which means it is illegal

>> No.2634106

>>2634088
It's not written in the rules that I can't ask a question they can't answer.

>> No.2634164

>>2634106
it says you must ask yes no questions, when you ask a question which has a correct answer of "maybe" it is not a yes no question and is thus illegal

>> No.2634172

>>2634047
see >>2633530

>> No.2634182

Who wants to know the answer?

>> No.2634189

>>2634172

Oh wait never mind.

>> No.2634199

dunno if someone posted yet, but I've constructed an answer.
1) A: If you were B, how would you answer the question 'Is the sky blue (or other trivially true question)?' ?
if A says 'da' or 'ja', then I know that word means 'no' goto X
if B answers some way other than 'da' or 'ja' or does not answer, then B must be the random god. goto Y
X: 2) B: Is the sky blue (or any other trivially true question)? if he answers truthfully, he tells truths, otherwise he speaks falses.
3) B: Is A the random god? we already know if he will speak truthfully or not, so finding the real answer is trivial, C is the remainder.
Y: 2) A: If you were C, how would answer the question 'is the sky blue (or other..)?' ? now we have the word for falseness
3) A: If you were C, how would you answer the question 'is A the truth god?' if A answers false, then he is the truth god, if he answers true, then he is the false god.

This rests on the assumption that gods cannot predict the future, although I think I can engineer the first question to take that possibility into account.

>> No.2634200

>>2632509
Wrong.

It just means you can't ask 2 of the gods the same question without spending 2 of your questions.

>> No.2634209

Ask God A and B and C who C is if C was lying.

>> No.2634218

>>2634209
that's not a yes or no question.

>> No.2634223

>>2634200
>Responding to a statement from five hours ago
>It's already been pointed out as wrong many times

>> No.2634225
File: 18 KB, 300x400, 1265208026783.jpg [View same] [iqdb] [saucenao] [google]
2634225

Working out what the rules to the scenario are is the real logic puzzle

>> No.2634231

>each question must be put to exactly one god.

idiots, this only means you only get one answer per question.

>> No.2634241

>>2634199
ah, if I rephrase the first question as "If you were B and B was not the random god, how would you answer the question 'Is the sky blue?' ?" then it does not depend on my assumption about the unpredictability of hidden random answers

>> No.2634242

>>2634199
this doesn't work, if A is random then you get no information from the first question, furthermore, as it is stated it is not strictly a yes/no question.

>> No.2634256

1. Ask any god "What would the random god say if I asked soandsoquestion"

If any answer, that god is the random god. Go to 2I

The other two gods will remain silent. Go to 2II

2I: Ask each remaining god "If I told you the sky is blue, would the other god answer "ja""

The false god would lie and say "da"

The truth god would know the false god would lie and say no, so the truth god say "da" means.

If ja was no, the opposite would happen: they would both answer "Ja"

2II: Still thinking about this, since you have to come up with two questions to determine which god is the random god, what the other one is (true/false), and what da/ja means. As is, if ever posed with this situation in real life for some reason or another, I have a 1/3 chance of this working.

>> No.2634270

>>2634256
you can't ask a question that is not strictly yes/no, so your first question is invalid. you're like the fourth person to make this same mistake.

>> No.2634277

1. a) do you like icecream?
33%prob. da
b) do you like icecream?
33% da
c) do you like icecream?
33% da
The others are true and false.. then.,
Ask God A: What would B say...


Rules match up? I was too lazy to completely understand this shit

>> No.2634278

>>2634242
>no information from 'random' god
not true, the random god randomly decides to answer truthfully or falsely, he either gives the true answer or the false answer, he does NOT randomly answer 'da' or 'ja'
>not a strictly yes or no question
yes it is, I ask, given some conditions, how the god would answer a yes or no question, the only two possible answers are 'yes' or 'no'. If you say a question that can not have a consistent answer cannot be asked, then I have the much more powerful tool of attempting to ask questions but not being able to, since my ability to ask questions depends on the status of the gods.

>> No.2634289

>>2634256
your first question doesn't work how you expect it to, the random god randomly decides to speak truthfully or falsely, he doesn't randomly say their word 'yes' or 'no'

>> No.2634305

If you accept 'Will random god answer ja if ...' as a valid question then the solutions already been given:

>>2633129
>>2633675

>> No.2634308

>>2634270

Then simply rephrase the question to a strictly y/n question.

"I have five fingers on one hand, ja/da?"

>> No.2634325

>>2634242
>>2634278
oh wait, i think i see what you're saying about the first question, then i would just need to phrase it as "If <conditions>, then would you say the sky is blue?" then the question is definitely a yes/no question.

>> No.2634348

>>2634278
>not true, the random god randomly decides to answer truthfully or falsely, he either gives the true answer or the false answer, he does NOT randomly answer 'da' or 'ja'
That doesn't matter, if A is random and B is true then A will answer your first question by randomly answering either yes or no. thus you can't conclude that the answer you get from this means no.

>yes it is, I ask, given some conditions, how the god would answer a yes or no question, the only two possible answers are 'yes' or 'no'. If you say a question that can not have a consistent answer cannot be asked, then I have the much more powerful tool of attempting to ask questions but not being able to, since my ability to ask questions depends on the status of the gods.

The way I see it is that a yes/no question must be either definitely yes or definitely no and if you try to ask a question that is not strictly yes/no then you automatically lose, this isn't clarified in the OP but it makes for a more sensible question.

>> No.2634355

>>2634325

Yeah, except since shade can make things a bit blurry, a better question would be something definitive, like "I have one skull, I have two thumbs, I have two feet, one plus one equals two," or something to that effect.

>> No.2634359

1. Ask 1st god: "Will B and C ever answer the same?"
2. Ask 2nd god: 'Will A and C ever answer the same?"
3. Ask whichever god you determine not to be random "Will you ever answer the same as (another god)"

Doesn't help with the da/ja though.

>> No.2634376

>>2634348
Oh wait, I see the problem now.

>> No.2634408

1. Ask A- Are you a God?
2. Ask A- Is B a God?
If different, you know A is random
not sure where to take it from here.

>> No.2634414

I can't think of a question that would find out who the Random god is. Once you find that out, the rest is really easy.

As someone said before, if you figure out Random in one question, True/False become easy. Just ask:

1) If I said the sky is blue, would you answer "ja?"
2) Is the sky blue?

True answers both with the same answer. False will have different answers.

>> No.2634469

>>2634414
you can distinguish between true and false in one question by asking "does ja mean yes?'

see my solution >>2633756 for how to figure out random.

>> No.2634492

>>2634469
i dont understand how your first question works

>> No.2634623

Thread went cold, so i read the solution and now my brain is more scrambled trying to understand it than figuring it out. I hate you OP, i'm going to bed

>> No.2634786

>>2634408
Random could also give you the same answer twice and then you would have no idea if it was random or not

>> No.2635094 [DELETED] 

derp

>> No.2636424

derp

>> No.2637604

derp