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A grok is a grok is a ... ? (Posted on 2007-06-29) Difficulty: 3 of 5
One day you meet three persons, each either a Knight or a Liar. You ask "How many of you are knights?", and the first person answers "Grok!".

Not understanding, you ask the second one "What does 'Grok' mean?", and he answers "One", but then the third one cries out "That's false!".

What can you tell about each person, if anything?

No Solution Yet Submitted by Federico Kereki    
Rating: 3.0000 (4 votes)

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Possible solution. | Comment 6 of 11 |
Assuming liars always lie and knights always tell the truth...

If the first person is a knight than the answer "grok" would be the correct number of knights. The second person states grok is one and the third person states that the second statement is false.

Forgetting the first person's answer until the end, either the second person is telling the truth or lying.
If the second person is telling the truth then grok is one...
But then the 3rd person is lying when he proclaims the statement false and the first person lied when he said there was one knight, as both he and the 2nd person would be knights...  Knights cannot lie. Therefore the second person must be lying, which means the 3rd person is a knight.
At this point the solution is obvious, but to wrap it up, Grok cannot be either one or zero; it cannot be one as we have already proven, two persons would be telling the truth (knights) for grok to be one and by virtue of the premise that would make one of them a liar. Nor can all of the persons be liars since the 3rd person declared the second person's statement a lie, and if all were liars that would be a liar telling the truth.

Nor can all the persons be knights, their statements do not all agree. The only possible number of knights is 2 and the only two statements which do not conflict and persons 1 and 3.

Therefore the first and 3rd persons are knights, and the second person is a liar.

  Posted by John Morris on 2007-06-30 03:14:55
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