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 Post subject: Very Confusing Logic Puzzle
PostPosted: Sat Oct 30, 2010 2:24 am 
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I am absolutely stumped. If you've got it, post your answer in white so its not spoiled for everyone else.

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 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.

Ive heard of and solved a similar riddle before with only a true speaking person and a false speaking person who both answer yes or no in english. Try this one first if the other is frustrating you.

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 Post subject: Re: Very Confusing Logic Puzzle
PostPosted: Sat Oct 30, 2010 10:45 am 
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dannyb21892 wrote:
Ive heard of and solved a similar riddle before with only a true speaking person and a false speaking person who both answer yes or no in english. Try this one first if the other is frustrating you.
Yeah, that part is very easy. I though finding the random would be hard, but it wasn't as bad as I thought. You just have to leverage what you know about the first two to identify the random one.

A = True
B = False
C = Random

Question 1: Identify what word means yes. The True and False Gods will both say Yes
Are you the Truth god?
A = Yes
B = Yes
C = Yes (no info here) / No (you've identified the Random god)

Question 2: Identify the True/False. Ask a question that is always true and you know the answer to.
Is the sky blue?
A = Yes
B = No
C = Yes/No

Based on Random, we will be able to either clearly identify the True or False god. If there was only 1 Yes, that one is the True god. If there
We will as a different question based on what answer was only given once.
Question 3A: If there was only 1 Yes to question 2: Ask if one of the no's is the Random God. We don't really know so I'll duplicate this for both B/C.
Is B the random god?
A = No (this tells us B is not the random god, so B = No, C = Random)
B = Yes
C = Yes/No

Is C the random god?
A = Yes (this tells us B is the random god, so B = No, C = Random)
B = Yes
C = Yes/No

Now we do a similar thing for if there was only 1 No
Question 3B: Is A the random god?
A = No
B = Yes (we know B lies, so A = True, C = Random)
C = Yes/No

Is C the random god?
A = Yes
B = No (we know B lies, so A = True, C = Random)
C = Yes/No

*edit* Apparently I'm asking too many questions so this solution doesn't work.

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Last edited by GuiltyBystander on Sat Oct 30, 2010 4:36 pm, edited 1 time in total.

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 Post subject: Re: Very Confusing Logic Puzzle
PostPosted: Sat Oct 30, 2010 2:35 pm 
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Just ask all three if they always lie :lol:

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 Post subject: Re: Very Confusing Logic Puzzle
PostPosted: Sat Oct 30, 2010 3:33 pm 
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dannyb21892 wrote:
I am absolutely stumped.
It's very tough, that's for sure. I don't see how a solution is possible. My reasoning is as follows: With 3 binary Ja/Da questions, if we can rely on consistent answers then there are 2^3 = 8 combinations of answers allowing the theoretical possibility of sorting out which god is which, because there are 3! = 6 possible permutations of True, False, and Random. However, because Random by definition answers randomly, he could give an answer the same as True or False would give and so we cannot identify Random after the 1st response if it turns out that our 1st question is to him. But if we can't be sure of receiving a consistent answer to our 1st question, we lose half of our 2^3 = 8 combinations of answers and we are down to 2^2 = 4, and no matter how ingenious our followup questions are, how can we distinguish between 6 permutations with a truth table containing only 4 cells?!?! I don't see how we could tell who Random is from the 2nd question and glean additional information which in combination with the 3rd question sorts out True from False. If there is a solution, I must be missing something very sneaky here.

Edit: :idea: I was forgetting about gaining a combination of clues from a single but compound question, which I believe must be key...

@GuiltyBystander, the crucial quote here is:
dannyb21892 wrote:
each question must be put to exactly one god.
I looked at your solution out of curiosity and it seems that you are posing three questions to all three gods, effectively asking nine questions, which is disobeying the constraints of the puzzle.


Last edited by Julian on Sat Oct 30, 2010 4:26 pm, edited 1 time in total.

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 Post subject: Re: Very Confusing Logic Puzzle
PostPosted: Sat Oct 30, 2010 4:22 pm 
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Julian wrote:
@GuiltyBystander, the crucial quote here is:
dannyb21892 wrote:
each question must be put to exactly one god.
I looked at your solution out of curiosity and it seems that you are posing three questions to all three gods, effectively asking nine questions, which is disobeying the constraints of the puzzle.

Awe, I missed that... Okay now I'm stumpted... have to think about it more.

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 Post subject: Re: Very Confusing Logic Puzzle
PostPosted: Sat Oct 30, 2010 5:15 pm 
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This is a VERY tricky logic puzzle. I do want to point out a few things that need clarification (after coming up with my own answer the first time I heard this, I did some research on this particular question and that is where I found these discrepancies)

Does Random randomly decide whether he will speak truthfully or falsely in response to each question? Or does he randomly spout of ja or da without listening to the question? (You could exploit this by asking an impossible question, the two non-random gods will be unable to answer but Random will happily spout of ja or da without listnening to the question. You could exploit the other case by asking each God to respond in their present state of mind, in which case Random will be locked into whichever personality trait, i.e. true or false, he has already chosen)

How does a God react to an impossible question? ex) Will you answer the word that means no in your language to this question? (True will be unable to correctly answer this question, so if a God is unable to answer this question and Random randomly spouts of ja or da without listening to the question, you have identified True)

How does a God react if he doesn't know the answer to the question? ex) Will that* God answer ja to the question is the sky blue (*pointing at Random) ? (Since Random's answers cannot be predicted by the other two Gods, they will not know how to answer)


I have tried to give examples that do not give away any solutions and just fyi for each case you can choose from above, there is an answer. Granted depending on how the rules above are stated the answers change, but seems to always be an answer.

IF YOU ASSUME AN IMPOSSIBLE-TO-ANSWER QUESTION WILL RESULT IN YOUR IMMEDIATE DEATH (and thus you don't want to ask anyone an impossible question) THERE IS STILL AN ANSWER SO DON'T THINK YOU MUST EXPLOIT THIS FACT TO SOLVE THE PUZZLE! This is true if Random chooses to act either as a true or as a false OR if he ignores the question and randomly spouts of ja or da. The harder case is if he randomly says ja or da. However the original problem actually clarifies Random's behavior as randomly acting as a liar or truth-teller

Again, this is a VERY tricky logic puzzle, but there is a legitimate answer that does not exploit impossible questions and for either of the above described behaviors of random.

Good Luck!
-Matt Galla
Ok, just to prove I am not making this up, here is the full answer for the hardest puzzle variation in which impossible questions are NOT allowed and Random ignores every question and randomly responds in ja or da: Label the Gods A, B, C. Question 1) Ask God A: "If I asked you 'Is God B random?' would you say 'da'?" Question 2a) If God A answered "da" to Question 1, ask God C: "If I asked you 'Are you True?' would you say 'da'?" Question 2b) If God A answered "ja" to Question 1, ask God B: "If I asked you 'Are you True?' would you say 'da'?" (same as 2a, just to a different God) Question 3) Ask the same God that you asked Question 2: "If I asked you 'Is A Random?' would you say 'da'?" Once you get the answer to the third question you can identify all three Gods. Now if anyone is cheating and reading this answer, you will have to figure out for yourself WHY this works. Otherwise you will probably have done enough thinking to already know why. Enjoy! ;P


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 Post subject: Re: Very Confusing Logic Puzzle
PostPosted: Sat Oct 30, 2010 5:41 pm 
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I have figured out a sort-of solution but I don't know if it counts as "cheating" or not! I have caught sight of part of Matt's post, and I'm pretty sure he discusses it. Anyway, my somewhat dubious attempted solution is in invisible ink:

Label the gods #1, #2, and #3. Ask #1: "If I asked #2 if he is True or Ja means Yes, would he answer Ja?" And again replacing with (#2, #3) and (#3, #1). The dubious trick is that because I didn't specify "...could he answer..." or "...would he sometimes answer..." or "...would he always answer...", when the question is being asked of how Random would respond, the questioned god remains silent because a clear Ja or Da response cannot be given. So, silence means the referred god is Random, and of the other two answers, the construction of the questions ensures that a Ja answer means the answering god is True, and a Da answer means the answering god is False.

Right, now I shall enjoy reading Matt's post. :)

Edit: And I see Matt assures us there is a non-dubious answer -- excellent, thanks! Okay, phew, back to the drawing board.


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 Post subject: Re: Very Confusing Logic Puzzle
PostPosted: Mon Nov 01, 2010 12:22 pm 
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You can totally find a solution to this one on wikipedia.

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 Post subject: Re: Very Confusing Logic Puzzle
PostPosted: Mon Nov 01, 2010 6:37 pm 
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theVDude wrote:
You can totally find a solution to this one on wikipedia.
:shock: Thanks, but I really wanted to figure it out on my own, which I did this evening. When I stopped thinking about possible questions for a while, and focussed instead on the logical best case scenario of what could be learned from the 1st Q&A, and the 2nd, a solution fell into place for me fairly soon afterwards, without any impossible/trick questions. :)


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 Post subject: Re: Very Confusing Logic Puzzle
PostPosted: Thu Nov 04, 2010 6:17 pm 
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As this is a very tricky puzzle, and I came close to giving up on it, for Danny and anyone else who feels like giving it (another) try, here are some hints that I hope will be helpful:

Assume that after the first question has been answered, you can identify a god who is definitely not Random. Put aside the first question and trust that when you come back to it later, you will be able to figure out a suitable question.

Work out a second question, which you put to a god who is either True or False, who you can identify for certain by the response.

Work out a third question, which you put to True or False, whose identity you know following the second question and answer, which allows you to identify the other two gods.

When you have succeeded in finding suitable second and third questions, return to the first question. Think of various statements, when they are true or false, how each god would answer, and of ways of asking about a combination of statements in a single question.

* It is not necessary to determine the meaning of Ja and Da to identify the gods.

* It is not necessary to ask a god how another god would answer a question.

I hope these help, and that I haven't given too much away.

-----------------------------------------------------------------------------

Here is another puzzle that I really like, which is similar in a way:

You have twelve identical-looking coins, one of which is counterfeit. The counterfeit coin is either heavier or lighter than the rest. The only scale available is a simple balance. Using the scale only three times, find the counterfeit coin. [For simplicity, number the coins 1 to 12.]


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 Post subject: Re: Very Confusing Logic Puzzle
PostPosted: Thu Nov 04, 2010 6:42 pm 
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I'll give the god puzzle another go, thanks :]

For your other puzzle, are all 11 other cons exactly alike in weight?

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 Post subject: Re: Very Confusing Logic Puzzle
PostPosted: Thu Nov 04, 2010 6:43 pm 
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Julian wrote:
-----------------------------------------------------------------------------

Here is another puzzle that I really like, which is similar in a way:

You have twelve identical-looking coins, one of which is counterfeit. The counterfeit coin is either heavier or lighter than the rest. The only scale available is a simple balance. Using the scale only three times, find the counterfeit coin. [For simplicity, number the coins 1 to 12.]


Highlight to show answer (I think its missing some parts though):
You take coins 1-4 and weigh them against coins 5-8, if they are equal then weigh coins 9 and 10 against coins 10 and 8 (we know this is a good coin), if they balance, then coin 12 is counterfeit; if either of the sides are uneven then weight 9 and 10, if they balance, then 11 is counterfeit; if they don't then either 9 or 10 is counterfeit (we don't know if the counterfeit is heavier or lighter). If the first weighing was uneven, then weigh 1, 2, 5 against 3, 6, and 9, if they balance, then weigh 7 and 8, if they balance, then 4 is counterfeit, if they don't then either 7 or 8 is counterfeit; if the second weighing is uneven then weigh 1 and 2, the same way you would weigh 7 or 8 (if they balance, then 6 is counterfeit...); or you could weigh 3 against a good coin, if it balances, then 5 is the counterfeit, if they don't then 3 is counterfeit.

Ps. Anyone know the color code for invisible text for twisty?(The gray posts, and no it's not gray)

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Last edited by MonkeyZ on Thu Nov 04, 2010 7:46 pm, edited 1 time in total.

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 Post subject: Re: Very Confusing Logic Puzzle
PostPosted: Thu Nov 04, 2010 7:06 pm 
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On white:
#FFFFFF would be this color

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I don't know half of you half as well as I should like and I like less than half of you half as well as you deserve.


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 Post subject: Re: Very Confusing Logic Puzzle
PostPosted: Thu Nov 04, 2010 7:07 pm 
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On gray:
This color is #EEEEEE.

Figured it out. Highlight above.

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