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This is an easy one, so try to do it in your head, without tabulating all the possible answers.
* * * *
Day-Nights and Night-Knights.
You are a sorcerer travelling by torch-light through the perpetual darkness of Agartha—the mythical subterranean world of Germanic legend. The magic spell that will transport you back to the Earth’s surface must be performed at night; however, owing to said perpetual darkness, it is impossible to tell whether it is night or day. In one of the sepulchres, you meet a knight on horseback.
‘Excuse me,’ you ask politely, ‘Is it true that the Knights of Agartha always know whether it is day or night? ’
‘True as the nose on your face!’ says the knight, drawing himself up.
‘Well, in that case, would you mind telling me whether...’
‘It is night!’ interrupts the knight. ‘But I feel it is my duty to add that Agartha is inhabited by two kinds of knights: The Day-Knights and Night-Knights. Day-Knights lie at night and speak the truth by day, and Night-Knights lie during the day and speak the truth at night.’
‘Oh, I see. And which are you?’
‘Bah! A Day-Knight, of course!’ says the knight angrily, and rides off at a trot into the darkness.
Will you perform your spell?
* * * *
Note: It is possible to determine from the knight's answers to your questions whether it is night or day and what kind of knight he was.
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Pooh-Bah
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Here is my answer in white text to avoid spoilers:
A Day-Knight would always claim that it is day, saying so truthfully during the day and as a lie at night. Vice-versa for the Night-Knight. Our Knight has revealed himself to be the latter by announcing that it is night, so he must be lying when he says he is a Day-Knight. Since he is lying, it must daytime so I would not cast my spell.
The real question is, which goblet contains the iocaine powder?
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Carpal Tunnel
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Carpal Tunnel
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BUT! If he is a Night Knight he lies half the time, so his answer to the first question might be a lie. AND if he is a Night Knight his avowal that Day Knights tell the truth in daylight and lie at night, etc. might also be a lie.
Hydra has fallen into the same fallacy as I discussed in the prior thread. You MUST have these statements coming from a trusted third party or they cannot be relied upon.
Edit:
The first question is whether the knights always know whether it is day or night up above in the outside world.
Last edited by TEd Remington; 12/24/06 05:04 PM.
TEd
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Pooh-Bah
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Yes I see your point. I was going with the flow and accepting certain statements as somehow above suspicion, e.g. the nature of Day Knights and Night Knights. Perhaps they are really fairies and our "underworld traveler" is really just in a dream and will fall in love with the first person he sees upon waking.
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Do the Night-Knights wear jim-jams?
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Quote:
Hydra has fallen into the same fallacy as I discussed in the prior thread. You MUST have these statements coming from a trusted third party or they cannot be relied upon.
In the prior thread (q.v.), the "fallacy" you accuse me of falling into was, in fact, the answer I eventually gave to the question of why Sarah's formulation failed. Now, if I'd given away the answer in my first post, it wouldn't have been much of a riddle, would it?
Of course, I have already said this. But why let the fact get in the way of a riposte that makes you look clever?
However, in this case you are right. I recalled the riddle from memory, and made this mistake: that the information about the Knights in this problem is meant to be a known-known.
Mutatis mutandis, Alex Williams's solution is correct.
Quote:
Solution
It is day, and the knight was a Night-Knight. This is easily realised by tabulating all the possible of answers of Night-Knights and Day-Knights at night and during the day:
DAY
Day-Knight: 'I am a Day-Knight. It is day.'
Night-Knight: 'I am a Day-Knight. It is night.'
NIGHT
Night-Knight: 'I am a Night-Knight. It is night.'
Day-Knight: 'I am a Night-Knight. It is day.'
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