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7 replies to this topic

#1 bonanova

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Posted 09 January 2008 - 06:15 PM

In the weird land of KKL, Knights always tell the truth, Knaves alternately tell the truth and lie and Liars always lie.
You have been sent on assignment to KKL to learn the ways of the natives and explore ways of identifying their type.

A guide leads you to a dark alley and introduces you to Al, Bob and Chuck, who agree to answer exactly three questions.

It's too dark to see their faces, you don't know which type of citizen each is, you can't tell which of them is speaking, and they reply in random order. Although they answer anonymously, you must determine which type of citizen they are.

You decide to start with the direct approach and then play it by ear:

[1] I'd like to know what type of citizens I'm talking with. Please tell me.

Sure thing. Myself, I'd be misleading you if I didn't tell you I'm a knight.
Hate to admit it, but I'm the unreliable one, being as how I'm a knave.
Don't listen to anything I tell you mate, I'm a bloody liar.

[2] OK great, thanks for that. But I wonder whether there really is one of each type.
Maybe there's more than one of some type. Can you comment specifically on that?

Pretty shrewed, aren't you? Well, you're right - it turns out we're all the same type.
Forget him. We told you already: there's exactly one of each type here.
Aww, they're both messing with you: actually, there's exactly two of one type here.

[3] OK well that's pretty confusing. For a final question, it might help just to talk about Al.
Would you tell me what type of citizen Al is? I think that will tell me all I need to know.


Why all the attention for Al? He's just a knave.
No way! Al is a liar!
Well I'll tell you this much, whatever Al is, Bert Bob is something else.

OK guys, thanks a lot.
I think now I know what type Chuck is.
And let's see ... what type Al is ... and also Bob.


Are you messing with us, or do you really know?
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The greatest challenge to any thinker is stating the problem in a way that will allow a solution.
- Bertrand Russell

#2 spoxjox

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Posted 09 January 2008 - 10:39 PM

I spent a long time typing up an involved reply. A few minutes before finishing it off, my computer reset itself. So I'm not going to attempt a response again until I get home after work, which may be very late in the day or even tomorrow (or later). For now:
Spoiler for spoxjox

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#3 unreality

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Posted 10 January 2008 - 12:10 AM

This looks hard :)

I will attempt soon
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#4 bonanova

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Posted 10 January 2008 - 06:57 AM

I spent a long time typing up an involved reply. A few minutes before finishing it off, my computer reset itself. So I'm not going to attempt a response again until I get home after work, which may be very late in the day or even tomorrow (or later). For now:

Spoiler for spoxjox

Remember knaves alternately tell the truth and lie.
After their first response they're deterministic.

Hint: use Notepad and save often, then copy into your reply.
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The greatest challenge to any thinker is stating the problem in a way that will allow a solution.
- Bertrand Russell

#5 unreality

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Posted 10 January 2008 - 09:22 PM

So let me get this right: Knaves do either of the following for three questions:

lie-truth-lie
OR
truth-lie-truth

Am I getting that right?
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#6 Writersblock

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Posted 11 January 2008 - 12:53 AM

Well I'll tell you this much, whatever Al is, Bert is something else.


Do you mean Bob, or is this a lie based on the wrong name, or irrelevant because of the wrong name?
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#7 srt_anon

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Posted 11 January 2008 - 01:33 AM

Great Puzzle.... I think I have it...

Spoiler for Solution


And here is why...
Spoiler for Logic


Question for you... what is chance Al is the Lying Knave (Lying in response to queries 1 and 3)?

Spoiler for Maybe Solution

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#8 bonanova

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Posted 11 January 2008 - 09:44 PM

Unreality asked:

So let me get this right: Knaves do either of the following for three questions:

lie-truth-lie
OR
truth-lie-truth

Am I getting that right?

Correct

Writersblock asked:

Do you mean Bob, or is this a lie based on the wrong name, or irrelevant because of the wrong name?

My bad. Bert/Bob is a typo.

Great Puzzle.... I think I have it...

Spoiler for Solution
And here is why...
Spoiler for Logic
You got it. Nice work.

Question for you... what is chance Al is the Lying Knave (Lying in response to queries 1 and 3)?
Spoiler for Maybe Solution

Interesting question.
Spoiler for Here's my answer

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The greatest challenge to any thinker is stating the problem in a way that will allow a solution.
- Bertrand Russell




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