Discussion about math, puzzles, games and fun.   Useful symbols: ÷ × ½ √ ∞ ≠ ≤ ≥ ≈ ⇒ ± ∈ Δ θ ∴ ∑ ∫ • π ƒ -¹ ² ³ °

You are not logged in.

## #1 2012-05-11 12:54:05

NNikolay
Novice

Offline

### The hardest logic puzzle ever becomes even tougher

Another variation of "Hardest logic puzzle ever" (viewtopic.php?id=10138)
This one is tougher, because we lose important information about Gods language. Previously we knew words "ja" and "da" but not their meaning. Now we know nothing about their language. I also changed clarifications to prohibit paradoxical questions that gods can't answer at all. But solution is still possible.

Full version:

“Three gods A, B, and C are called, in some 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. You do not know their language.”
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).
(2)    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)
(3)    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.
(4)    If you ask a question, where the god can’t give an answer, he will answer ‘no’.
(5)    All gods speak in the same language.”

PS How to post links here?

## #2 2012-05-15 08:30:41

mathgogocart
Super Member

Offline

### Re: The hardest logic puzzle ever becomes even tougher

to post links you have to be an established member

bbcode;.Uhhhhhhhhh im bored.
"Those who feed spambots are spambot conspiarators,and bad people." mathgogocart.

## #3 2012-06-01 00:40:37

wintersolstice
Real Member

Offline

### Re: The hardest logic puzzle ever becomes even tougher

I don't think this puzzle is theoritcally possible! (though I could be wrong:D)

Last edited by wintersolstice (2012-06-01 00:52:50)

Why did the chicken cross the Mobius Band?
To get to the other ...um...!!!

## #4 2012-06-09 20:35:05

NNikolay
Novice

Offline

### Re: The hardest logic puzzle ever becomes even tougher

Hi wintersolstice,

Your proof is based on the assumption that first of 3 questions can't give you any information except sample word from god's language. This is not correct. I mean, this is correct if you have one question only. But in our case you can get more information as a result of all 3 questions.

Last edited by NNikolay (2012-06-09 20:35:49)

## #5 2012-06-16 22:09:34

wintersolstice
Real Member

Offline

### Re: The hardest logic puzzle ever becomes even tougher

#### NNikolay wrote:

Hi wintersolstice,

Your proof is based on the assumption that first of 3 questions can't give you any information except sample word from god's language. This is not correct. I mean, this is correct if you have one question only. But in our case you can get more information as a result of all 3 questions.

what I assumed is that you were using the "one question to determine yes/no followed by two questions to work out who's who (which you've proved wrong:D)

however the reason I believed that is because:

I tried the original solution on this version and realised that when you ask the first question (because you don't know any words) you can't actually find any information from the first question apart from a sample word even after the second tow questions.

here the original solution and you see if you can find information form the first question

this is just one solution but you'll find that using this solution is impossible on your version.

the only thing I can suggest is:

write down your own solution of 3+ question showing what the questions are asked to who and what in cirscumstances is each question asked(without showing anyone of course) and see if it works for all 6 possibilites (of who's who) and all possible answers and true and false questions and what is yes and no etc), this way you know it has a solution:D. That's what I did when I posted my variation of the puzzle:D

btw when I posted my proof I only said I don't "think" it's impossibe I never said I "know" it's impossible:D and it was imcomplete so hopefully I have completed it now:D

Last edited by wintersolstice (2012-06-16 22:19:25)

Why did the chicken cross the Mobius Band?
To get to the other ...um...!!!

## #6 2012-06-19 12:08:32

NNikolay
Novice

Offline

### Re: The hardest logic puzzle ever becomes even tougher

OK.
Here is my

But there is another modification with beautiful solution. Basically the same setup with the following assumptions:
2.    God’s reply two different unknown words for Yes and No. Head explosion is clearly different from any answer when you see it. But you can’t ask this god second time
3.    Random answers randomly Yes or No regardless the question. As a result his head can’t explode.
4.    You need a solution in two questions.

## #7 2012-06-20 01:00:42

wintersolstice
Real Member

Offline

### Re: The hardest logic puzzle ever becomes even tougher

#### NNikolay wrote:

4.    You need a solution in two questions.

but that's impossible, it can't be done in two questions, look at my "proof" above it shows that two question isn't enough, if you need it explaining I'll try and explain it better for you:D

try out EVERY combination of answers you get from the two questions (that give you information) and see if that can tell you who's who, some combinations will tell you but some combinations won't.

btw I haven't looked at your solution yet but with my proof I don't think I need to.

Why did the chicken cross the Mobius Band?
To get to the other ...um...!!!

## #8 2012-06-20 12:56:37

NNikolay
Novice

Offline

### Re: The hardest logic puzzle ever becomes even tougher

Wintersolstice, I have showed how your proof is wrong and have given a solution. What else can I do?

Second modification has a solution too. 2 questions with 3 possible outcomes give 9 combinations! Of course you loose some information due to Random behaving really randomly and because you don't know the words upfront. But it is enough to separate 6 cases.

Hope you will read the solution before telling it's wrong

## #9 2012-06-20 22:09:50

wintersolstice
Real Member

Offline

### Re: The hardest logic puzzle ever becomes even tougher

#### NNikolay wrote:

Wintersolstice, I have showed how your proof is wrong and have given a solution. What else can I do?

Second modification has a solution too. 2 questions with 3 possible outcomes give 9 combinations! Of course you loose some information due to Random behaving really randomly and because you don't know the words upfront. But it is enough to separate 6 cases.

Hope you will read the solution before telling it's wrong

I completely misread your last post that's all:D When you said "modification" I thought you meant you had modifiyed your original solution! and when you posted your "second modification" I thought it was describing your solution! (giving clues I mean:D)

anyway I've had a look at the solution but it's going to take a bit of time to get my head round it (although this has ruined for me! Nevermind there's the other puzzle)

btw have you seen my "variation" that I mentioned early (it's not that difficult really though)

Last edited by wintersolstice (2012-06-20 22:10:33)

Why did the chicken cross the Mobius Band?
To get to the other ...um...!!!