a logic puzzle

[Sylvia Else]

Sylvia Else wrote:
) Willem wrote:
)> Oh I had forgotten that. Slight amendment:
)>
)> Ask Person 1 the following question:
)> "What would Person 2 answer if I asked him if he is a Knight ?"
)
)> In case of silence, ask Person 3 the following question:
)> "What would Person 1 answer if I asked him if he is a Knight ?"
)
)> Else ask Person 2 the following question:
)> "What would Person 3 answer if I asked him if he is a Knight ?"
)

Look at question 1 again.

Let's try that again.

If I ask a Knight whether a Knave would say he's a Knight - the Knave
would say yes, so the Knight would say yes. If I ask a Knave whether a
Knight would say that he's a Knight, the Knight would say yes, so the
Knave would say no.

Considering the permuatations, R randomizer, T knighT, E knavE, and the
resulting answers, ? = Y/N, - = no answer.

R T E ? Y (Q2 is to P2 about P3).
R E T ? N ditto.
T R E - N (Q2 is to P3 about P1).
E R T - Y ditto.
T E R N - (Q2 is to P2 about P3).
E T R Y - ditto.

Yes, seems OK.

Sylvia.

 

[Willem]

Sylvia Else wrote:
) Willem wrote:
)> Sylvia Else wrote:
)> ) So we know that p2 is not the randomizer. Silence from p2 indicates that
)> ) p3 is the randomizer. Unfortunately, we're out of questions, and we
)> ) still don't know which way round p1 and p2 are.
)>
)> Look at question 1 again.
)
) Let's try that again.

I actually meant that quite literally.
'We don't know which way round p1 and p2 are':

Looking at question 1 (which was answered 'yes' or 'no'), with the
additional information that p1 is not a randomizer, you can deduce
if p1 is Knave or Knight.


SaSW, Willem
--
Disclaimer: I am in no way responsible for any of the statements
made in the above text. For all I know I might be
drugged or something..
No I'm not paranoid. You all think I'm paranoid, don't you !
#EOT

 

[Wanderer]

Dodekachotomy Island

On Dodekachotomy Island are four types of people

Normals:
Who answer Yes, No or No Response.
Nymphs:
Who will never say No. Only Yes or No Response.
Nay Sayers:
Who will never say Yes. Only No or No Response.
Nincompoops:
Who will never say anything.

They belong to three Orders

Knights:
Who will never Lie.
Knaves:
Who will never tell the Truth.
Know Nots:
Who don't believe there any difference between truths and lies.

Know Not Normals will answer all questions randomly Yes or No.
Know Not Nymphs answer Yes to any question.
Know Not Nay Sayers answer No to any question.
Know Not Nincompoops never say anything.

The people of Dodekachotomy Island know all about each other and the
rules of the Orders.
They understand English perfectly but refuse to speak it using only
the words for Yes and No
from their language which you don't know.
They are also experts on the nature of lies and truth and logic.
And they know all the normal stuff like over, under, before, after,
up, down, numbers, the alphabet, etc.

On Dodekachotomy Island there is door with a combination lock which
leads off the island.
In front of the door stand twelve guards, one of each type and order
combination.
The guards wear identical suits of armor except for a letter engraved
on the breast plate.
The letters are A thru L. You may write down one question on a slip of
paper. Hand it to guard A,
who will respond or not depending on the question, hand the slip to
guard B who will respond or not
and hand the letter to the next guard and so on until all the guards
have had a chance to respond.

Only the Nymph that will say yes to anything, knows the combination
and will open the door for you.

What question should you write down to find the Nymph that always says
yes?

 

[Sylvia Else]

Sylvia Else wrote:
) Willem wrote:
)> Sylvia Else wrote:
)> ) So we know that p2 is not the randomizer. Silence from p2 indicates that
)> ) p3 is the randomizer. Unfortunately, we're out of questions, and we
)> ) still don't know which way round p1 and p2 are.
)>
)> Look at question 1 again.
)
) Let's try that again.

I actually meant that quite literally.
'We don't know which way round p1 and p2 are':

Looking at question 1 (which was answered 'yes' or 'no'), with the
additional information that p1 is not a randomizer, you can deduce
if p1 is Knave or Knight.

Yes, I know. But having reached the wrong conclusion once, I wanted to
be sure I hadn't missed something else.

Sylvia.

 

[[email protected]]

You know the puzzles involving Dichotomy Island, inhabited
by knights and knaves, who will answer any yes/no question;
knights are honest, knaves are compulsive liars.

Now, let's welcome onto the island, the randomizers -
they answer any question yes or no, 50-50.

You are marooned on Trichotomy Island. You meet 3
inhabitants. You are given that one is a knight, another
a knave, the other a randomizer. You are permitted 2
questions, each question addressed to a single (not
both the same) person, and must determine their
identities.

with 6 possible arrangements and only two bits of information there is
no way to identify all the people.

 

[James Dow Allen]

Nymphs:
        Who will never say No.

I believe there are more appropriate venues for solicitations
of this ilk.


BTW, I was disappointed no one revived my "Knarks"
Message <[email protected]>
who always make statements in pairs, one true, one false.
I think the latest Dell Logic Magazine has one of my
Knights, Knaves & Knarks puzzles.

James Dow Allen

 

[Willem]

Robert Baer wrote:
) Sorry; randomizer bu definition picks "yes" or "no" randomly; NO silence.

Stating some well-known fact about the puzzle 4 times in a row as 'proof'
that a method doesn't work doesn't make the objection any more valid.

So tell me, why does the fact that the randomizer always answers make this
method invalid ?

After all, the Knave and Knight *can* answer with silence.
(And by the rules of the revised puzzle, they *will* if they cannot
determine the answer to the question asked.)


SaSW, Willem
--
Disclaimer: I am in no way responsible for any of the statements
made in the above text. For all I know I might be
drugged or something..
No I'm not paranoid. You all think I'm paranoid, don't you !
#EOT

 

[Wanderer]

Holy cow!

So, just to clarify a bit (not that I think I'll be the one solving
this)...

If you ask a Knight Nay Sayer, "Does 2+2=4?", he'll say nothing?
(i.e., "No Response" means that the guy remains silent?)

If you ask a Knave Normal, "Does 2+2=4?", he'll say either "Onk" or
"Bonk," whichever one is the word for "No" in their language?

After you've gotten all of your answers, you'll tap one of the 12
people on the shoulder, and if you've tapped the one and only "Know
Not Nymph," then he'll open the door for you?

It would be great if there were some elegant question that will get
you 9 silences, 2 Onks and a Bonk, and you can then deduce that the
Bonk came from the "Know Not Nymph."'

However, I think this is going to be a very hairy answer, involving a
lot of truth tables.  After all, the "Know Not Normal" could easily
answer the same way as the "Know Not Nymph," so you have to rely on
others to point out the "Know Not Nymph" for you.

Yes. The guards will only give a response if it doesn't violate their
Code. So a Knight Nay Sayer will only say No. If No is not a lie and
Knave Nay Sayer will only say No if it is not the truth. They will
give No Response if the answer should be Yes to fulfill the
requirements of their code or if the answer is indeterminate. They
are in the same position as you are where your answer would be wrong
if it assumed that the Know Not Normal will say specifically Yes or No
on any specific occasion.

Good Luck
http://en.wikipedia.org/wiki/Knights_and_knaves

 

[Willem]

Robert Baer wrote:
) ...revised?
) Allowable answers: "yes" and "no"; allowable questions: only those
) that canbe answered with a "yes" or a "no".
) So, what am i missing?

The bit where we very clearly and obviously stated that we were talking
about the revised puzzle where, if a Knight or Knave cannot answer a yes/no
question by their truth/lie rules, they remain silent.


SaSW, Willem
--
Disclaimer: I am in no way responsible for any of the statements
made in the above text. For all I know I might be
drugged or something..
No I'm not paranoid. You all think I'm paranoid, don't you !
#EOT

 

[Sylvia Else]

Answer would never be silence; randomizer picks random answer by
definition...

The answer can be silence if the question is not asked of the randomizer.

Sylvia.

 

[Wanderer]

The answer can be silence if the question is not asked of the randomizer.

Sylvia.

Yes, it's explained at the end of this Wiki as the exploding God-Head.

http://en.wikipedia.org/wiki/The_hardest_logic_puzzle_ever

In A simple solution to the hardest logic puzzle ever,[2] B. Rabern
and L. Rabern develop the puzzle further by pointing out that it is
not the case that 'ja' and 'da' are the only possible answers a god
can give. It is also possible for a god to be unable to answer at all.

 

[George Weinberg]

OR... There's no solution. I never remember to consider the date
when I see what looks like a cool puzzle.

Still, I'd love to run a couple questions through a simulator and see
what kind of results I get. "If I asked you if the Know Not Nymph
were standing within two people of you, what would you say?" and so
on.


And I like the idea of a Knight/Knave puzzle where you don't know
their language!

Ask Guy #1: "Are you a knight?" Answer: "Onk."
Ask Guy #2: "Did he say he was a knight?" Answer: "Bonk."

It's not as bad as you think.

If it weren't for the normal numbskull, it would be easy. Just ask
something like "are you something other than a knight", and the knights and
knaves would say no (or remain silent) as would the naysaying numbskull,
the nymph numbskull would be the only one saying yes.

But since you've got a normal numbskull who will (maybe) say yes,there's no
hope of guranteeing onkly one yes. So what you have to do is, guarentee
that there are at most two yesses (the normal and nymph numbskulls), there
are at least three noes (so you can distinguish between yes and no), and
the exact number of noes depends on whether the question is put to the
normal numbskull before or after the nymph numbskull.

Working out the details is fairly straightforward but tedious, but it
shouldn't be too hard to come up with a compound question which the normal
and naysaying knaves will always answer no to and the normal and naysaying
knights will say no if the nymph numbskll is asked first and and remain
silent if the normal numbskull.

George

 

[Willem]

Robert Baer wrote:
) Willem wrote:
)> The bit where we very clearly and obviously stated that we were talking
)> about the revised puzzle where, if a Knight or Knave cannot answer a yes/no
)> question by their truth/lie rules, they remain silent.
)>
)>
)> SaSW, Willem
) ...hmmm....would that also imply that the randomizer could choose to
) "answer" likewise???

No.


SaSW, Willem
--
Disclaimer: I am in no way responsible for any of the statements
made in the above text. For all I know I might be
drugged or something..
No I'm not paranoid. You all think I'm paranoid, don't you !
#EOT