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 A grok is a grok is a ... ? (Posted on 2007-06-29)
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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 I give up. | Comment 9 of 11 |

Assuming first is a knight, he can only reply unknown or 2. 0 is excluded as he would be a knight. 1 is excluded because then either second or third is telling the truth in addition to first. 3 is excluded as either second or third is telling a lie. Either first response sets up the second to be a liar and the third to be a knight.

Assuming first is a liar, only the 1 is excluded because then the second would be the only knight but  the first would be telling the truth also.

Assuming the first is a liar and the number of knights are unknown to the first then the first must respond with 0, 2, or 3 and the second continues to be a liar with the third being a knight.

Assuming the first is a liar and the number of knights are known to the first then the first must respond with an incorrect response among unknown, 0, 2, or 3 but not a 1, and the second continues to be a liar with the third being a knight.

Assuming the first is a knight and the number of knights are known to the first then the first must respond with 2 and the second is a liar and the third a knight.

Assuming the first is a knight and the number of knights are unknown to the first then the first must respond with unknown but the second remains a liar with the third a knight.

The second is a liar. The third is a knight. The first is unknown or even if he knows the answer to the original question.

 Posted by Ross Maier on 2007-07-01 19:14:36

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