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18 replies to this topic

#11 araver

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Posted 24 November 2010 - 11:03 PM

Sorry I didn't attempt the first two. So I have a question
Is there a rule to govern the answering of random answerer ? Like 1 time he speaks truth while 2 time he lies? or something like that?


Do the liars and truth tellers know what the random answer will answer for a given question?

Or in another way of asking it. Is the random answer for a particular question predetermined such that if I go to a truth teller and ask him what the random answerer will answer to a particular question and then go to the random answerer and ask him that question they will always be the same answer?

Asked to truth teller "If I next ask him (the random answerer) if he is a liar what will be his answer ?"

Truth teller: True

Asked to specified random answerer "Are you a liar?"

Random answerer: True

The answer will still be random to us it just means that the liar, truth teller and random answerer have access to the same random number table.


I believe there are several classical definitions for random answerers in these types of puzzles.

RandomFlipFlop: He doesn't look at the question. First time he flips a coin then simply says alternatively either Yes or No.

RandomWeak: Before answering a question he tosses a coin. If it is heads he lies, if it is tails he tells the truth.

RandomStrong: He doesn't look at the question, simply flips a coin and says either Yes or No.

I believe bushindo's random's are RandomStrong (from the wording of the puzzle) since this is the most challenging situation of the three :D
So randoms are not predictable by others and their answers don't depend on their previous answers.

EDIT: Just seen that bushindo already posted a reply.

Edited by araver, 24 November 2010 - 11:05 PM.

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#12 phaze

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Posted 25 November 2010 - 01:13 AM

Let's say that the liars and the truth tellers do not know what the random answerers would respond to any given question. I think the question is more challenging that way.

Then going by rule number 3 we cant ask anyone what answer anyone else can give unless we a sure that we are either asking about a truth-teller / liar or asking the question to a random answerer?
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#13 bushindo

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Posted 25 November 2010 - 01:32 AM

Then going by rule number 3 we cant ask anyone what answer anyone else can give unless we a sure that we are either asking about a truth-teller / liar or asking the question to a random answerer?


Yes, we can't ask anyone what answer someone else will give to a particular question, unless we are sure that we are either asking about a truth-teller / liar or asking the question to a random answerer.
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#14 araver

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Posted 25 November 2010 - 01:38 AM

Then going by rule number 3 we cant ask anyone what answer anyone else can give unless we a sure that we are either asking about a truth-teller / liar or asking the question to a random answerer?


Yup ... or else his head might explode :D

Seriously, yes, you cannot ask that kind of questions (according to most opinions out there) since they force a third type of answer: either "I do not know" or "I can't answer" or head-exploding (I like this one most of all).

It's similar to a Turing machine or a program that has at least one branch that does not terminate (loops).
On the right input, it will give you a Yes/No answer (sooner or later)
On the wrong input, you might be waiting for an eternity without knowing for sure if it's going to respond eventually. You could ask it whether Fermat's Last Theorem is true (which would take a while, but eventually the machine would say Yes) or if P=NP (and still wait for the response as I'm doing now :D).
Safe bet is to try only question that can be answered in all cases.
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#15 araver

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Posted 25 November 2010 - 02:24 AM

My first strategy
Spoiler for

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#16 bushindo

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Posted 25 November 2010 - 03:50 AM

My first strategy

Spoiler for


Excellent strategy! I didn't realize that it could be done in 9. After reading your post, I re-examined my strategy and realized that there was an inefficient part that essentially wasted 1 question, hence my limit of 10. Great work and thanks for that detailed post. I learned something new today.

Alternative strategy
Spoiler for

Edited by bushindo, 25 November 2010 - 03:56 AM.

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#17 araver

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Posted 25 November 2010 - 05:08 AM

Spoiler for Nice one

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#18 bushindo

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Posted 25 November 2010 - 08:20 AM

Spoiler for Nice one


That's an interesting issue you bring up, I'll have to think about it some. I'm glad you like the puzzle. I greatly enjoy your insights on this puzzle. I have another one that is similar to this but with a twist. However, I'm going on vacation tomorrow and I probably won't be able check this board for the next few days, so I'll post the puzzle next week.

Edited by bushindo, 25 November 2010 - 08:22 AM.

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#19 araver

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Posted 25 November 2010 - 12:53 PM

I realized I haven't told why I expected my first hunch to work. It might be worth something so I'm sharing it.

Spoiler for

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Almost random quotes:
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